100 results found for "coterminal" in all classes.
D. \(\frac{29\pi}{18}\)
ऋणात्मक कोण में \(2\pi\) जोड़ें। \(-\frac{7\pi}{18}+2\pi=\frac{29\pi}{18}\) मिलता है। / Add \(2\pi\) to the negative angle. \(-\frac{7\pi}{18}+2\pi=\frac{29\pi}{18}\).
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A. \(\frac{\pi}{4}\)
अंतर \(\frac{5\pi}{2}-2\theta\) को \(2\pi\) का गुणज होना चाहिए। दिए अंतराल में \(\theta=\frac{\pi}{4}\) उपयुक्त है। / The difference \(\frac{5\pi}{2}-2\theta\) must be a multiple of \(2\pi\). In the given interval \(\theta=\frac{\pi}{4}\) is suitable.
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If the difference between two angles is \(1980^\circ\) can they be coterminal?
D. नहीं क्योंकि \(\frac{1980}{360}\) पूर्णांक नहीं हैNo because \(\frac{1980}{360}\) is not an integer
सहप्रारंभी कोणों का अंतर \(360^\circ\) का पूर्णांक गुणज होता है। \(\frac{1980}{360}=\frac{11}{2}\) पूर्णांक नहीं है। / The difference of coterminal angles is an integer multiple of \(360^\circ\). \(\frac{1980}{360}=\frac{11}{2}\) is not an integer.
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If \(7x+10^\circ\) and \(2x-50^\circ\) are coterminal then what is the least positive value of (x)?
C. \(60^\circ\)
अंतर \(5x+60^\circ\) है और यह \(360^\circ\) का गुणज होना चाहिए। सबसे छोटे धनात्मक मान के लिए \(x=60^\circ\) है। / The difference is \(5x+60^\circ\) and it must be a multiple of \(360^\circ\). For the least positive value \(x=60^\circ\).
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Which angle is coterminal with \(\frac{5\pi}{8}\) and lies between \(-4\pi\) and \(-2\pi\)?
D. \(-\frac{27\pi}{8}\)
\(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\) है। यह दिया गया अंतराल पूरा करता है। / \(\frac{5\pi}{8}-4\pi=-\frac{27\pi}{8}\). This satisfies the given interval.
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What is the least positive coterminal angle of \(-1025^\circ\)?
C. \(55^\circ\)
\(-1025^\circ+1080^\circ=55^\circ\) है। नकारात्मक बड़े कोण में \(360^\circ\) के गुणज जोड़ें। / \(-1025^\circ+1080^\circ=55^\circ\). Add multiples of \(360^\circ\) to a large negative angle.
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C. \(120^\circ\)
अंतर \(4\theta-120^\circ\) को \(360^\circ\) का गुणज होना चाहिए। सबसे छोटे धनात्मक मान के लिए \(\theta=120^\circ\) है। / The difference \(4\theta-120^\circ\) must be a multiple of \(360^\circ\). For the least positive value \(\theta=120^\circ\).
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B. \(395^\circ\)
\(35^\circ+360^\circ=395^\circ\) दिए अंतराल में आता है। सहप्रारंभी कोण के लिए \(360^\circ\) जोड़ें या घटाएं। / \(35^\circ+360^\circ=395^\circ\) lies in the given interval. Add or subtract \(360^\circ\) for coterminal angles.
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What is the coterminal angle of \(-\frac{41\pi}{9}\) between (0) and \(2\pi\)?
D. \(\frac{13\pi}{9}\)
\(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\) है। नकारात्मक कोण में \(2\pi\) के गुणज जोड़ें। / \(-\frac{41\pi}{9}+6\pi=\frac{13\pi}{9}\). Add multiples of \(2\pi\) to a negative angle.
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Which of the following angles is not coterminal with \(210^\circ\)?
D. \(\frac{5\pi}{6}\)
\(210^\circ=\frac{7\pi}{6}\), जबकि \(\frac{5\pi}{6}=150^\circ\) है। परीक्षा में सभी विकल्पों को एक ही इकाई में बदलकर तुलना करें। / \(210^\circ=\frac{7\pi}{6}\), while \(\frac{5\pi}{6}=150^\circ\). In exams, convert all options into the same unit before comparing.
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B. \(-27^\circ\)
चौथे चतुर्थांश का मुख्य कोण \(333^\circ\) है और उसका सबसे बड़ा ऋणात्मक सह-प्रारंभिक कोण \(333^\circ-360^\circ=-27^\circ\) है। परीक्षा में सबसे बड़ा ऋणात्मक कोण \(-360^\circ\) से ऊपर रखें। / The principal angle in the fourth quadrant is \(333^\circ\), and its greatest negative coterminal angle is \(333^\circ-360^\circ=-27^\circ\). In exams, keep the greatest negative angle above \(-360^\circ\).
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If \(\theta\) is coterminal with \(\frac{58\pi}{9}\) and \(0<\theta<2\pi\), what is \(\theta\)?
A. \(\frac{4\pi}{9}\)
\(\frac{58\pi}{9}-6\pi=\frac{4\pi}{9}\)। परीक्षा में \(2\pi\) के गुणज घटाकर अंतराल में कोण रखें। / \(\frac{58\pi}{9}-6\pi=\frac{4\pi}{9}\). In exams, subtract multiples of \(2\pi\) to keep the angle in the interval.
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B. (4)
एक पूर्ण चक्कर \(360^\circ\) होता है और \(\frac{1440^\circ}{360^\circ}=4\)। परीक्षा में अंतर को \(360^\circ\) से भाग दें। / One complete revolution is \(360^\circ\) and \(\frac{1440^\circ}{360^\circ}=4\). In exams, divide the difference by \(360^\circ\).
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What is the coterminal angle between \(0^\circ\) and \(360^\circ\) for \(-1540^\circ\)?
A. \(260^\circ\)
\(-1540^\circ+1800^\circ=260^\circ\), इसलिए मुख्य सह-प्रारंभिक कोण \(260^\circ\) है। परीक्षा में ऋणात्मक कोण में \(360^\circ\) के गुणज जोड़ें। / \(-1540^\circ+1800^\circ=260^\circ\), so the principal coterminal angle is \(260^\circ\). In exams, add multiples of \(360^\circ\) to negative angles.
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Which of the following pairs consists of coterminal angles?
A. \(45^\circ\) और \(405^\circ\)\(45^\circ\) and \(405^\circ\)
\(405^\circ-45^\circ=360^\circ\) है इसलिए दोनों सहप्रारंभी हैं। अंतर \(360^\circ\) का गुणज होना चाहिए। / \(405^\circ-45^\circ=360^\circ\) so they are coterminal. The difference must be a multiple of \(360^\circ\).
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What is the least positive coterminal angle of \(1490^\circ\)?
B. \(50^\circ\)
\(1490^\circ-1440^\circ=50^\circ\) है। \(360^\circ\) के अधिकतम संभव गुणज को घटाएं। / \(1490^\circ-1440^\circ=50^\circ\). Subtract the largest possible multiple of \(360^\circ\).
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If \(\theta=-315^\circ\) then what is its coterminal angle in \(0^\circ\le\theta<360^\circ\)?
B. \(45^\circ\)
\(-315^\circ+360^\circ=45^\circ\) है। दिए गए अंतराल में लाने के लिए \(360^\circ\) जोड़ें। / \(-315^\circ+360^\circ=45^\circ\). Add \(360^\circ\) to bring it into the given interval.
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What is the coterminal angle of \(-\frac{23\pi}{6}\) between (0) and \(2\pi\)?
A. \(\frac{\pi}{6}\)
\(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\) है। नकारात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें। / \(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\). Add multiples of \(2\pi\) to a negative radian angle.
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If \(\theta=110^\circ\) then what is the general form of all coterminal angles of \(\theta\)?
B. \(110^\circ+360^\circ k\)
डिग्री में सहप्रारंभी कोण \(360^\circ\) के गुणज जोड़कर मिलते हैं। इसलिए रूप \(110^\circ+360^\circ k\) है। / In degrees coterminal angles are obtained by adding multiples of \(360^\circ\). So the form is \(110^\circ+360^\circ k\).
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\(\frac{13\pi}{6}\) is coterminal with which smaller positive angle?
A. \(\frac{\pi}{6}\)
\(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\) है। \(2\pi\) घटाकर मुख्य कोण प्राप्त करें। / \(\frac{13\pi}{6}-2\pi=\frac{\pi}{6}\). Subtract \(2\pi\) to obtain the principal angle.
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What is the coterminal angle of \(\frac{19\pi}{4}\) between (0) and \(2\pi\)?
C. \(\frac{3\pi}{4}\)
\(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\) है। \(2\pi\) के गुणज घटाकर मुख्य कोण पाएं। / \(\frac{19\pi}{4}-4\pi=\frac{3\pi}{4}\). Subtract multiples of \(2\pi\) to get the principal angle.
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How will all coterminal angles of \(-\frac{3\pi}{4}\) be written?
B. \(-\frac{3\pi}{4}+2n\pi\)
सहप्रारंभी कोणों में \(2\pi\) के पूर्ण गुणज जोड़े जाते हैं। इसलिए रूप \(-\frac{3\pi}{4}+2n\pi\) है। / Coterminal angles are formed by adding integral multiples of \(2\pi\). Hence the form is \(-\frac{3\pi}{4}+2n\pi\).
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What is the least positive coterminal angle of \(920^\circ\)?
C. \(200^\circ\)
\(920^\circ-720^\circ=200^\circ\) होता है। बड़े कोण में \(360^\circ\) के गुणज घटाएं। / Since \(920^\circ-720^\circ=200^\circ\). Subtract multiples of \(360^\circ\) from large angles.
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What is the coterminal angle of \(-\frac{7\pi}{6}\) between \(0^\circ\) and \(360^\circ\)?
B. \(150^\circ\)
\(-\frac{7\pi}{6}=-210^\circ\) और \(360^\circ\) जोड़ने पर \(150^\circ\) मिलता है। नकारात्मक कोण में \(360^\circ\) जोड़कर मुख्य कोण खोजें। / \(-\frac{7\pi}{6}=-210^\circ\) and adding \(360^\circ\) gives \(150^\circ\). For a negative angle add \(360^\circ\) to get the principal angle.
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C. \(180^\circ\)
\(540^\circ-360^\circ=180^\circ\)। परीक्षा में दिए अंतराल के अनुसार मुख्य कोण चुनें। / \(540^\circ-360^\circ=180^\circ\). In exams, choose the principal angle according to the given interval.
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If \(\theta=-\frac{17\pi}{4}\), what is the coterminal angle between (0) and \(2\pi\)?
D. \(\frac{7\pi}{4}\)
\(-\frac{17\pi}{4}+6\pi=\frac{7\pi}{4}\)। परीक्षा में ऋणात्मक कोण में \(2\pi\) के गुणज जोड़ें। / \(-\frac{17\pi}{4}+6\pi=\frac{7\pi}{4}\). In exams, add multiples of \(2\pi\) to a negative angle.
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C. (4)
एक पूर्ण चक्कर \(2\pi\) होता है, इसलिए \(\frac{8\pi}{2\pi}=4\)। परीक्षा में रेडियन में पूर्ण चक्कर को \(2\pi\) याद रखें। / One complete rotation is \(2\pi\), so \(\frac{8\pi}{2\pi}=4\). In exams, remember that a full rotation in radians is \(2\pi\).
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What is the positive coterminal angle between (0) and \(2\pi\) for the angle \(-\frac{7\pi}{6}\)?
A. \(\frac{5\pi}{6}\)
धनात्मक सह-प्रारंभिक कोण पाने के लिए \(2\pi\) जोड़ते हैं। परीक्षा में ऋणात्मक कोण को पहले मुख्य अंतराल में बदलिए। / Add \(2\pi\) to get the positive coterminal angle. In exams, first convert a negative angle to the principal interval.
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Which angle is coterminal with \( -75^\circ \)?
B. \(285^\circ\)
\(-75^\circ+360^\circ=285^\circ\) है। सहसमापी कोणों का अंतर \(360^\circ\) का गुणज होता है। / \(-75^\circ+360^\circ=285^\circ\). Coterminal angles differ by a multiple of \(360^\circ\).
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A. \( \frac{\pi}{4} \)
\( \frac{9\pi}{4}-2\pi=\frac{\pi}{4} \) है। \(2\pi\) घटाकर सहसमापी मानक कोण पाएं। / \( \frac{9\pi}{4}-2\pi=\frac{\pi}{4} \). Subtract \(2\pi\) to find the coterminal standard angle.
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If \(3\theta+45^\circ\) and \(\theta-135^\circ\) are coterminal, what is one value of \( \theta \)?
A. \(90^\circ\)
(3\theta+45^\circ-\(\theta-135^\circ\)=360^\circ) से \(2\theta+180^\circ=360^\circ\) और \( \theta=90^\circ \) है। अंतर को \(360^\circ\) का गुणज रखें। / (3\theta+45^\circ-\(\theta-135^\circ\)=360^\circ) gives \(2\theta+180^\circ=360^\circ\) and \( \theta=90^\circ \). Keep the difference as a multiple of \(360^\circ\).
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D. \(90^\circ\)
सहसमापी होने पर अंतर \(360^\circ\) हो सकता है इसलिए \(5x+20^\circ=x+380^\circ\) से \(x=90^\circ\) है। रैखिक समीकरण बनाएं। / For coterminal angles the difference can be \(360^\circ\), so \(5x+20^\circ=x+380^\circ\) gives \(x=90^\circ\). Form a linear equation.
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What is the principal coterminal angle of \( -\frac{49\pi}{12} \) between (0) and \(2\pi\)?
C. \( \frac{11\pi}{12} \)
\( -\frac{49\pi}{12}+\frac{60\pi}{12}=\frac{11\pi}{12} \) है। ऋणात्मक रेडियन कोण में \(2\pi\) के पर्याप्त गुणज जोड़ें। / \( -\frac{49\pi}{12}+\frac{60\pi}{12}=\frac{11\pi}{12} \). Add enough multiples of \(2\pi\) to a negative radian angle.
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What is the coterminal angle of \(-1855^\circ\) between \(0^\circ\) and \(360^\circ\)?
C. \(305^\circ\)
\(-1855^\circ+2160^\circ=305^\circ\) है। बड़े ऋणात्मक कोण में \(360^\circ\) का उपयुक्त गुणज जोड़ें। / \(-1855^\circ+2160^\circ=305^\circ\). Add a suitable multiple of \(360^\circ\) to a large negative angle.
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What is the principal coterminal angle of \(2210^\circ\)?
B. \(50^\circ\)
\(2210^\circ-2160^\circ=50^\circ\) है। मुख्य कोण के लिए \(360^\circ\) के गुणज घटाएं। / \(2210^\circ-2160^\circ=50^\circ\). Subtract multiples of \(360^\circ\) to find the principal angle.
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What is the coterminal angle of \( \frac{37\pi}{12} \) between (0) and \(2\pi\)?
A. \( \frac{13\pi}{12} \)
\( \frac{37\pi}{12}-\frac{24\pi}{12}=\frac{13\pi}{12} \) है। रेडियन में \(2\pi\) के गुणज घटाएं। / \( \frac{37\pi}{12}-\frac{24\pi}{12}=\frac{13\pi}{12} \). Subtract multiples of \(2\pi\) in radians.
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What is the coterminal angle of \( \frac{29\pi}{4} \) between (0) and \(2\pi\)?
A. \( \frac{5\pi}{4} \)
\( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \) है। रेडियन में \(2\pi=\frac{8\pi}{4}\) घटाते हैं। / \( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} \). In radians subtract \(2\pi=\frac{8\pi}{4}\).
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What is the principal coterminal angle of \( -1430^\circ \)?
D. \(10^\circ\)
\( -1430^\circ+1440^\circ=10^\circ \) है। निकटतम बड़े \(360^\circ\) के गुणज को जोड़ना आसान है। / \( -1430^\circ+1440^\circ=10^\circ \). Adding the nearest larger multiple of \(360^\circ\) is easy.
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Which is the coterminal angle of \( -1000^\circ \) between \(0^\circ\) and \(360^\circ\)?
B. \(80^\circ\)
\( -1000^\circ+1080^\circ=80^\circ \) है। ऋणात्मक बड़े कोणों में \(360^\circ\) के गुणज जोड़ें। / \( -1000^\circ+1080^\circ=80^\circ \). Add multiples of \(360^\circ\) for large negative angles.
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What is the coterminal angle of \(985^\circ\) between \(0^\circ\) and \(360^\circ\)?
A. \(265^\circ\)
\(985^\circ-720^\circ=265^\circ\) है। बड़े कोण से \(360^\circ\) के उपयुक्त गुणज घटाएं। / \(985^\circ-720^\circ=265^\circ\). Subtract a suitable multiple of \(360^\circ\) from a large angle.
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What is the coterminal angle of \( \frac{25\pi}{6} \) between (0) and \(2\pi\)?
A. \( \frac{\pi}{6} \)
\( \frac{25\pi}{6}-\frac{24\pi}{6}=\frac{\pi}{6} \) है। रेडियन में \(2\pi\) घटाकर मुख्य कोण निकालें। / \( \frac{25\pi}{6}-\frac{24\pi}{6}=\frac{\pi}{6} \). Subtract \(2\pi\) in radians to find the principal angle.
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What will be the principal coterminal angle of \( -1020^\circ \)?
D. \(60^\circ\)
\( -1020^\circ+1080^\circ=60^\circ \) है। ऋणात्मक बड़े कोणों में \(360^\circ\) के उचित गुणज जोड़ें। / \( -1020^\circ+1080^\circ=60^\circ \). Add a suitable multiple of \(360^\circ\) for large negative angles.
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Which is the positive coterminal angle of \( -780^\circ \)?
B. \(300^\circ\)
\( -780^\circ+1080^\circ=300^\circ \) होता है। \(360^\circ\) बार-बार जोड़कर धनात्मक मान पाएं। / \( -780^\circ+1080^\circ=300^\circ \). Add \(360^\circ\) repeatedly to get a positive value.
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What is the coterminal angle of \(840^\circ\) between \(0^\circ\) and \(360^\circ\)?
D. \(120^\circ\)
\(840^\circ-720^\circ=120^\circ\) है। बड़े कोण से \(360^\circ\) के गुणज घटाएं। / \(840^\circ-720^\circ=120^\circ\). Subtract multiples of \(360^\circ\) from a large angle.
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What is the coterminal angle of \(420^\circ\) between \(0^\circ\) and \(360^\circ\)?
C. \(60^\circ\)
\(420^\circ-360^\circ=60^\circ\) है। सहसमापी कोण पाने के लिए \(360^\circ\) घटाएं। / \(420^\circ-360^\circ=60^\circ\). Subtract \(360^\circ\) to get a coterminal angle.
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What is the coterminal angle of \(750^\circ\) between \(0^\circ\) and \(360^\circ\)?
A. \(30^\circ\)
\(750^\circ-720^\circ=30^\circ\) है। बड़े कोण में \(360^\circ\) के गुणज घटाएं। / \(750^\circ-720^\circ=30^\circ\). Subtract multiples of \(360^\circ\) from large angles.
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What is the positive coterminal angle of \(-30^\circ\)?
C. \(330^\circ\)
\(-30^\circ+360^\circ=330^\circ\) है। ऋणात्मक कोण को धनात्मक बनाने के लिए \(360^\circ\) जोड़ें। / \(-30^\circ+360^\circ=330^\circ\). Add \(360^\circ\) to make a negative angle positive.
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Which is a negative coterminal angle of \(120^\circ\)?
B. \(-240^\circ\)
\(120^\circ-360^\circ=-240^\circ\) होता है। ऋणात्मक सहसमापी कोण पाने के लिए \(360^\circ\) घटाएं। / \(120^\circ-360^\circ=-240^\circ\). Subtract \(360^\circ\) to get a negative coterminal angle.
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Which is a positive coterminal angle of \(45^\circ\)?
C. \(405^\circ\)
\(45^\circ+360^\circ=405^\circ\) इसलिए यह सहसमापी कोण है। सहसमापी कोण के लिए \(360^\circ\) जोड़ें या घटाएं। / \(45^\circ+360^\circ=405^\circ\) so it is coterminal. Add or subtract \(360^\circ\) for coterminal angles.
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Which angle is a positive coterminal angle of \(-40^\circ\)?
C. \(320^\circ\)
\(-40^\circ+360^\circ=320^\circ\) होता है। धनात्मक सह-अंतिम कोण के लिए \(360^\circ\) जोड़ें। / \(-40^\circ+360^\circ=320^\circ\). Add \(360^\circ\) to get a positive coterminal angle.
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Which angle is a negative coterminal angle of \(65^\circ\)?
B. \(-295^\circ\)
\(65^\circ-360^\circ=-295^\circ\) होता है। ऋणात्मक सह-अंतिम कोण पाने के लिए \(360^\circ\) घटाएं। / \(65^\circ-360^\circ=-295^\circ\). Subtract \(360^\circ\) to get a negative coterminal angle.
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If an angle is \(-210^\circ\), what is its coterminal angle between \(0^\circ\) and \(360^\circ\)?
B. \(150^\circ\)
\(-210^\circ+360^\circ=150^\circ\) होता है। ऋणात्मक कोण में \(360^\circ\) जोड़ें। / \(-210^\circ+360^\circ=150^\circ\). Add \(360^\circ\) to a negative angle.
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What is the coterminal angle of \(-450^\circ\) between \(0^\circ\) and \(360^\circ\)?
C. \(270^\circ\)
\(-450^\circ+720^\circ=270^\circ\) होता है। जरूरत हो तो \(360^\circ\) एक से अधिक बार जोड़ें। / \(-450^\circ+720^\circ=270^\circ\). Add \(360^\circ\) more than once if needed.
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What is the coterminal angle of \(765^\circ\) between \(0^\circ\) and \(360^\circ\)?
B. \(45^\circ\)
\(765^\circ-720^\circ=45^\circ\) होता है। बड़े कोण से \(360^\circ\) के गुणज घटाएं। / \(765^\circ-720^\circ=45^\circ\). Subtract multiples of \(360^\circ\) from a large angle.
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What is the coterminal angle of \(-30^\circ\) between \(0^\circ\) and \(360^\circ\)?
D. \(330^\circ\)
\(-30^\circ+360^\circ=330^\circ\) होता है। ऋणात्मक कोण में \(360^\circ\) जोड़ें। / \(-30^\circ+360^\circ=330^\circ\). Add \(360^\circ\) to a negative angle.
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Which is a negative coterminal angle of \(45^\circ\)?
B. \(-315^\circ\)
\(45^\circ-360^\circ=-315^\circ\) होता है। ऋणात्मक सह-अंतिम कोण के लिए \(360^\circ\) घटाएं। / \(45^\circ-360^\circ=-315^\circ\). Subtract \(360^\circ\) to get a negative coterminal angle.
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Which is a positive coterminal angle of \(30^\circ\)?
A. \(390^\circ\)
\(30^\circ+360^\circ=390^\circ\) होता है। सह-अंतिम कोण के लिए \(360^\circ\) जोड़ें या घटाएं। / \(30^\circ+360^\circ=390^\circ\). Add or subtract \(360^\circ\) to get a coterminal angle.
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The difference between two coterminal angles is a multiple of what?
D. \(360^\circ\)
सह-अंतिम कोणों में अंतर \(360^\circ\) के पूर्णांक गुणज का होता है। अंतिम भुजा समान हो तो यह नियम लगाएं। / The difference between coterminal angles is an integral multiple of \(360^\circ\). Use this rule when the terminal side is the same.
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B. \(\frac{5\pi}{12}\)
पहले कोण का मान \(\frac{\pi}{4}\) और दूसरे का \(\frac{\pi}{6}\) है, इसलिए योग \(\frac{5\pi}{12}\) है। परीक्षा में दोनों कोणों को अलग-अलग घटाएं। / The first angle gives \(\frac{\pi}{4}\) and the second gives \(\frac{\pi}{6}\), so the sum is \(\frac{5\pi}{12}\). In exams, reduce both angles separately.
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What is the least positive coterminal angle of \(-1000^\circ\)?
C. \(80^\circ\)
\(-1000^\circ+1080^\circ=80^\circ\) है। परीक्षा में ऋणात्मक बड़े कोण में \(360^\circ\) के गुणज जोड़ें। / \(-1000^\circ+1080^\circ=80^\circ\). In exams, add multiples of \(360^\circ\) to a large negative angle.
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D. \(90^\circ\)
क्योंकि (a-b=4b) को \(360^\circ\) का गुणज होना चाहिए, सबसे छोटा \(b=90^\circ\) है। परीक्षा में सह-टर्मिनल शर्त को अंतर पर लगाएं। / Since (a-b=4b) must be a multiple of \(360^\circ\), the least \(b=90^\circ\). In exams, apply the coterminal condition to the difference.
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If \(\theta\) and \(\phi\) are coterminal angles, which expression must be an integer?
B. \(\frac{\theta-\phi}{2\pi}\)
सह-टर्मिनल कोणों का अंतर \(2\pi n\) होता है, इसलिए \(\frac{\theta-\phi}{2\pi}\) पूर्णांक होगा। परीक्षा में अंतर को देखें, योग को नहीं। / The difference of coterminal angles is \(2\pi n\), so \(\frac{\theta-\phi}{2\pi}\) is an integer. In exams, check the difference, not the sum.
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B. \(250^\circ\)
\(540^\circ\) का शेष \(180^\circ\) है, इसलिए \(180^\circ+\theta\equiv 70^\circ\) और \(\theta=250^\circ\) है। परीक्षा में पहले स्थिर भाग को घटाएं। / The remainder of \(540^\circ\) is \(180^\circ\), so \(180^\circ+\theta\equiv 70^\circ\) and \(\theta=250^\circ\). In exams, reduce the fixed part first.
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D. \(\frac{29\pi}{12}\)
\(75^\circ+360^\circ=435^\circ=\frac{29\pi}{12}\), जो \(2\pi\) और \(3\pi\) के बीच है। परीक्षा में दी गई सीमा के अनुसार चक्कर जोड़ें। / \(75^\circ+360^\circ=435^\circ=\frac{29\pi}{12}\), which lies between \(2\pi\) and \(3\pi\). In exams, add revolutions according to the given interval.
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Can two angles be coterminal if their difference is \(\frac{35\pi}{3}\)?
C. नहीं, क्योंकि यह \(2\pi\) का पूर्णांक गुणज नहीं हैNo, because it is not an integral multiple of \(2\pi\)
\(\frac{35\pi}{3}\div2\pi=\frac{35}{6}\), जो पूर्णांक नहीं है। परीक्षा में सह-टर्मिनल के लिए \(2\pi n\) जांचें। / \(\frac{35\pi}{3}\div2\pi=\frac{35}{6}\), which is not an integer. In exams, check \(2\pi n\) for coterminal angles.
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Which is the greatest negative angle greater than \(-360^\circ\) coterminal with \(845^\circ\)?
D. \(-235^\circ\)
\(845^\circ\) का धनात्मक प्रधान कोण \(125^\circ\) है, इसलिए ऋणात्मक सह-टर्मिनल कोण \(125^\circ-360^\circ=-235^\circ\) है। परीक्षा में ऋणात्मक उत्तर के लिए \(360^\circ\) घटाएं। / The positive principal angle of \(845^\circ\) is \(125^\circ\), so the negative coterminal angle is \(125^\circ-360^\circ=-235^\circ\). In exams, subtract \(360^\circ\) for the negative answer.
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What is the least positive coterminal angle of \(845^\circ\)?
A. \(125^\circ\)
\(845^\circ-720^\circ=125^\circ\) है। परीक्षा में \(360^\circ\) के निकटतम बड़े गुणज को घटाएं। / \(845^\circ-720^\circ=125^\circ\). In exams, subtract the nearest convenient multiple of \(360^\circ\).
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What is the least positive coterminal angle of \(\frac{31\pi}{7}\)?
A. \(\frac{3\pi}{7}\)
\(\frac{31\pi}{7}-4\pi=\frac{3\pi}{7}\) है। परीक्षा में \(2\pi\) के गुणज घटाते रहें। / \(\frac{31\pi}{7}-4\pi=\frac{3\pi}{7}\). In exams, keep subtracting multiples of \(2\pi\).
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Which of the following is not coterminal with \(\frac{5\pi}{4}\)?
B. \(-\frac{7\pi}{4}\)
सह-टर्मिनल कोणों का अंतर \(2\pi\) का पूर्णांक गुणज होना चाहिए। \(-\frac{7\pi}{4}\) का अंतर ऐसा नहीं है। / Coterminal angles must differ by an integral multiple of \(2\pi\). The difference for \(-\frac{7\pi}{4}\) does not satisfy this.
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Which is the least positive coterminal angle of \(-725^\circ\)?
D. \(355^\circ\)
\(-725^\circ\) में (3) बार \(360^\circ\) जोड़ने पर \(355^\circ\) मिलता है। परीक्षा में उत्तर को \(0^\circ\) से \(360^\circ\) के बीच रखें। / Adding \(360^\circ\) three times to \(-725^\circ\) gives \(355^\circ\). In exams, keep the answer between \(0^\circ\) and \(360^\circ\).
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C. (6)
दोनों को बराबर करने पर \(\frac{n\pi}{6}=\pi\) मिलता है। इसलिए (n=6) है। / Equating them gives \(\frac{n\pi}{6}=\pi\). Hence (n=6).
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If \( \theta=\frac{14\pi}{5} \), what is the principal coterminal angle of \( \theta-\pi \)?
D. \( \frac{9\pi}{5} \)
\( \theta-\pi=\frac{14\pi}{5}-\frac{5\pi}{5}=\frac{9\pi}{5} \) है और यह (0) से \(2\pi\) में है। पहले घटाव करें फिर सीमा देखें। / \( \theta-\pi=\frac{14\pi}{5}-\frac{5\pi}{5}=\frac{9\pi}{5} \), and it is in (0) to \(2\pi\). First subtract and then check the range.
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If \( \theta=\frac{11\pi}{9} \), what is the principal coterminal angle of \(2\theta\)?
B. \( \frac{4\pi}{9} \)
\(2\theta=\frac{22\pi}{9}\) और \( \frac{22\pi}{9}-2\pi=\frac{4\pi}{9} \) है। गुणा करने के बाद \(2\pi\) घटाएं। / \(2\theta=\frac{22\pi}{9}\) and \( \frac{22\pi}{9}-2\pi=\frac{4\pi}{9} \). After multiplying, subtract \(2\pi\).
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In which interval does the principal coterminal angle of \( -\frac{23\pi}{10} \) lie?
D. \( \frac{3\pi}{2}<\theta<2\pi \)
\( -\frac{23\pi}{10}+\frac{40\pi}{10}=\frac{17\pi}{10} \) है जो \( \frac{3\pi}{2} \) और \(2\pi\) के बीच है। पहले मुख्य कोण निकालें। / \( -\frac{23\pi}{10}+\frac{40\pi}{10}=\frac{17\pi}{10} \), which lies between \( \frac{3\pi}{2} \) and \(2\pi\). First find the principal angle.
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A. \( \frac{\pi}{6} \)
\( \frac{13\pi}{6}-2\pi=\frac{\pi}{6} \) है और यह प्रथम चतुर्थांश में है। पहले मुख्य कोण फिर संदर्भ कोण निकालें। / \( \frac{13\pi}{6}-2\pi=\frac{\pi}{6} \), and it is in the first quadrant. First find the principal angle and then the reference angle.
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What will be the principal coterminal angle of \( \frac{52\pi}{9} \)?
C. \( \frac{16\pi}{9} \)
\( \frac{52\pi}{9}-\frac{36\pi}{9}=\frac{16\pi}{9} \) है। \(2\pi=\frac{18\pi}{9}\) मानकर घटाएं। / \( \frac{52\pi}{9}-\frac{36\pi}{9}=\frac{16\pi}{9} \). Use \(2\pi=\frac{18\pi}{9}\) while subtracting.
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Which is the coterminal angle of \(-\frac{41\pi}{10}\) between (0) and \(2\pi\)?
B. \( \frac{19\pi}{10} \)
\(-\frac{41\pi}{10}+\frac{60\pi}{10}=\frac{19\pi}{10}\) है। ऋणात्मक कोण में \(2\pi\) के पर्याप्त गुणज जोड़ें। / \(-\frac{41\pi}{10}+\frac{60\pi}{10}=\frac{19\pi}{10}\). Add enough multiples of \(2\pi\) to a negative angle.
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\( -710^\circ \) gives a coterminal angle in which quadrant?
A. प्रथम चतुर्थांशFirst quadrant
\( -710^\circ+720^\circ=10^\circ \) है इसलिए अंतिम भुजा प्रथम चतुर्थांश में है। बड़े ऋणात्मक कोण में \(360^\circ\) के गुणज जोड़ें। / \( -710^\circ+720^\circ=10^\circ \), so the terminal side lies in the first quadrant. Add multiples of \(360^\circ\) to a large negative angle.
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Which is the principal coterminal angle of \( \frac{31\pi}{3} \)?
B. \( \frac{\pi}{3} \)
\( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \) है। \(2\pi=\frac{6\pi}{3}\) का गुणज घटाएं। / \( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} \). Subtract a multiple of \(2\pi=\frac{6\pi}{3}\).
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What is the coterminal angle of \( -\frac{19\pi}{6} \) between (0) and \(2\pi\)?
B. \( \frac{5\pi}{6} \)
\( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \) है। ऋणात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें। / \( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} \). Add multiples of \(2\pi\) to a negative radian angle.
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\( -310^\circ \) is coterminal with an angle in which quadrant?
A. प्रथम चतुर्थांशFirst quadrant
\( -310^\circ+360^\circ=50^\circ \) है और \(50^\circ\) प्रथम चतुर्थांश में है। सहसमापी कोण से चतुर्थांश आसानी से मिलता है। / \( -310^\circ+360^\circ=50^\circ \) and \(50^\circ\) lies in the first quadrant. The coterminal angle gives the quadrant easily.
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Which is the principal coterminal angle of \( \frac{14\pi}{3} \)?
C. \( \frac{2\pi}{3} \)
\( \frac{14\pi}{3}-\frac{12\pi}{3}=\frac{2\pi}{3} \) है। \(2\pi=\frac{6\pi}{3}\) लिखकर घटाएं। / \( \frac{14\pi}{3}-\frac{12\pi}{3}=\frac{2\pi}{3} \). Write \(2\pi=\frac{6\pi}{3}\) and subtract.
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What is the coterminal angle of \( -\frac{17\pi}{4} \) between (0) and \(2\pi\)?
B. \( \frac{7\pi}{4} \)
\( -\frac{17\pi}{4}+\frac{24\pi}{4}=\frac{7\pi}{4} \) है। ऋणात्मक रेडियन कोण में \(2\pi\) के गुणज जोड़ें। / \( -\frac{17\pi}{4}+\frac{24\pi}{4}=\frac{7\pi}{4} \). Add multiples of \(2\pi\) to a negative radian angle.
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What is the principal coterminal angle of \(1125^\circ\)?
C. \(45^\circ\)
\(1125^\circ-1080^\circ=45^\circ\) है। मुख्य कोण के लिए \(0^\circ\) से \(360^\circ\) की सीमा लें। / \(1125^\circ-1080^\circ=45^\circ\). For the principal angle use the range from \(0^\circ\) to \(360^\circ\).
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What is the coterminal angle of \(390^\circ\) between \(0^\circ\) and \(360^\circ\)?
B. \(30^\circ\)
\(390^\circ-360^\circ=30^\circ\) है। कोण को सीमा में लाने के लिए \(360^\circ\) घटाते रहें। / \(390^\circ-360^\circ=30^\circ\). Keep subtracting \(360^\circ\) to bring the angle into the range.
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Which coterminal angle of \(-120^\circ\) lies between \(0^\circ\) and \(360^\circ\)?
B. \(240^\circ\)
\(-120^\circ+360^\circ=240^\circ\) होता है। ऋणात्मक कोण को मुख्य दायरे में लाने के लिए \(360^\circ\) जोड़ें। / \(-120^\circ+360^\circ=240^\circ\). Add \(360^\circ\) to bring a negative angle into the principal range.
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What is the coterminal angle of \(400^\circ\) between \(0^\circ\) and \(360^\circ\)?
C. \(40^\circ\)
\(400^\circ-360^\circ=40^\circ\) होता है। बड़े कोण को \(360^\circ\) से घटाकर मुख्य कोण पाएं। / \(400^\circ-360^\circ=40^\circ\). Subtract \(360^\circ\) from a large angle to get the principal angle.
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In which quadrant will the terminal side of \(-1460^\circ\) lie?
D. चतुर्थFourth
\(-1460^\circ+1800^\circ=340^\circ\) है। \(340^\circ\) चतुर्थ चतुर्थांश में आता है। / \(-1460^\circ+1800^\circ=340^\circ\). \(340^\circ\) lies in the fourth quadrant.
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What is the correct relation between \(\frac{13\pi}{5}\) and \(-\frac{7\pi}{5}\)?
D. वे सह-प्रारंभिक हैंThey are coterminal
दोनों कोणों का अंतर \(4\pi\) है, जो \(2\pi\) का गुणज है। इसलिए वे सह-प्रारंभिक हैं। / The difference between the two angles is \(4\pi\), which is a multiple of \(2\pi\). Therefore, they are coterminal.
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What is the principal positive angle between (0) and \(2\pi\) for \(-\frac{31\pi}{6}\)?
B. \(\frac{5\pi}{6}\)
\(-\frac{31\pi}{6}\) में \(6\pi\) जोड़ने पर \(\frac{5\pi}{6}\) मिलता है। परीक्षा में ऋणात्मक कोण में \(2\pi\) के गुणज जोड़ें। / Adding \(6\pi\) to \(-\frac{31\pi}{6}\) gives \(\frac{5\pi}{6}\). In exams, add multiples of \(2\pi\) to negative angles.
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In which quadrant will the terminal side of \(-850^\circ\) lie?
C. तृतीयThird
\(-850^\circ+1080^\circ=230^\circ\) है। \(230^\circ\) तृतीय चतुर्थांश में आता है। / \(-850^\circ+1080^\circ=230^\circ\). \(230^\circ\) lies in the third quadrant.
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If two angles are \(\frac{5\pi}{7}\) and \(\frac{19\pi}{7}\), how are they related?
A. सह-प्रारंभिकCoterminal
अंतर \(\frac{14\pi}{7}=2\pi\) है, इसलिए दोनों सह-प्रारंभिक हैं। परीक्षा में अंतर को \(2\pi\) के गुणज से मिलाइए। / The difference is \(\frac{14\pi}{7}=2\pi\), so the angles are coterminal. In exams, match the difference with a multiple of \(2\pi\).
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If two angles measure \(410^\circ\) and \(-310^\circ\), which statement is correct about them?
A. वे सह-प्रारंभिक हैंThey are coterminal
(410^\circ-\(-310^\circ\)=720^\circ), जो \(360^\circ\) का गुणज है। परीक्षा में सह-प्रारंभिक कोणों का अंतर \(360^\circ k\) होता है। / (410^\circ-\(-310^\circ\)=720^\circ), which is a multiple of \(360^\circ\). In exams, coterminal angles differ by \(360^\circ k\).
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Which statement about \( \frac{29\pi}{12} \) and \( \frac{5\pi}{12} \) is correct?
A. वे सहसमापी हैंThey are coterminal
अंतर \( \frac{29\pi}{12}-\frac{5\pi}{12}=2\pi \) है इसलिए वे सहसमापी हैं। रेडियन में सहसमापी अंतर \(2\pi\) का गुणज होता है। / The difference \( \frac{29\pi}{12}-\frac{5\pi}{12}=2\pi \), so they are coterminal. In radians, coterminal angles differ by a multiple of \(2\pi\).
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If the difference between two angles is \(1080^\circ\), what is the correct statement about them?
C. वे सहसमापी होते हैंThey are coterminal
\(1080^\circ=3\times360^\circ\) है इसलिए ऐसे कोण सहसमापी होते हैं। अंतर \(360^\circ\) का गुणज हो तो अंतिम भुजा समान होती है। / \(1080^\circ=3\times360^\circ\), so such angles are coterminal. If the difference is a multiple of \(360^\circ\), the terminal side is the same.
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Which statement about \(1485^\circ\) and \(45^\circ\) is correct?
D. वे सहसमापी कोण हैंThey are coterminal angles
\(1485^\circ-45^\circ=1440^\circ=4\times360^\circ\) इसलिए वे सहसमापी हैं। अंतर \(360^\circ\) का गुणज हो तो सहसमापी मानें। / \(1485^\circ-45^\circ=1440^\circ=4\times360^\circ\), so they are coterminal. If the difference is a multiple of \(360^\circ\), consider them coterminal.
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Which statement about \(135^\circ\) and \(-225^\circ\) is correct?
B. वे सहसमापी कोण हैंThey are coterminal angles
(135^\circ-\(-225^\circ\)=360^\circ) है इसलिए वे सहसमापी कोण हैं। अंतर \(360^\circ\) का गुणज हो तो कोण सहसमापी होते हैं। / (135^\circ-\(-225^\circ\)=360^\circ), so they are coterminal angles. If the difference is a multiple of \(360^\circ\), the angles are coterminal.
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Which statement about \(725^\circ\) and \(5^\circ\) is correct?
B. वे सहसमापी कोण हैंThey are coterminal angles
\(725^\circ-5^\circ=720^\circ=2\times 360^\circ\) इसलिए वे सहसमापी हैं। अंतर \(360^\circ\) का गुणज हो तो कोण सहसमापी होते हैं। / \(725^\circ-5^\circ=720^\circ=2\times 360^\circ\) so they are coterminal. If the difference is a multiple of \(360^\circ\) the angles are coterminal.
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What type of angles can \(0^\circ\) and \(360^\circ\) be considered?
C. सहसमापी कोणCoterminal angles
\(0^\circ\) और \(360^\circ\) की अंतिम भुजा समान होती है इसलिए वे सहसमापी हैं। \(360^\circ\) के अंतर को पहचानें। / \(0^\circ\) and \(360^\circ\) have the same terminal side so they are coterminal. Look for a difference of \(360^\circ\).
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If two angles are \(20^\circ\) and \(380^\circ\), what is their relation?
A. वे सह-अंतिम कोण हैंThey are coterminal angles
\(380^\circ-20^\circ=360^\circ\) इसलिए दोनों सह-अंतिम कोण हैं। अंतर \(360^\circ\) का गुणज हो तो सह-अंतिम मानें। / \(380^\circ-20^\circ=360^\circ\), so they are coterminal angles. If the difference is a multiple of \(360^\circ\), they are coterminal.
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