principal-angle se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
19 questions tagged with principal-angle.
D. \(\frac{4\pi}{3}\)
दक्षिणावर्त कोण \(-\frac{14\pi}{3}\) है। इसमें \(6\pi\) जोड़ने पर \(\frac{4\pi}{3}\) मुख्य कोण मिलता है। / The clockwise angle is \(-\frac{14\pi}{3}\). Adding \(6\pi\) gives the principal angle \(\frac{4\pi}{3}\).
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B. \(\frac{7\pi}{6}\)
नेट कोण \(\frac{17\pi}{6}-\frac{5\pi}{3}=\frac{7\pi}{6}\) है। वामावर्त को धनात्मक और दक्षिणावर्त को ऋणात्मक लें। / The net angle is \(\frac{17\pi}{6}-\frac{5\pi}{3}=\frac{7\pi}{6}\). Take counterclockwise as positive and clockwise as negative.
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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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What is the principal angle of the fourth-quadrant ray of the line (y=-x)?
D. \(\frac{7\pi}{4}\)
चतुर्थ चतुर्थांश में (y=-x) की किरण का संदर्भ कोण \(\frac{\pi}{4}\) है। इसलिए मुख्य कोण \(\frac{7\pi}{4}\) है। / The fourth-quadrant ray of (y=-x) has reference angle \(\frac{\pi}{4}\). Hence the principal angle is \(\frac{7\pi}{4}\).
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What is the principal angle of the terminal side passing through the point (\(-\sqrt{3},1\))?
B. \(\frac{5\pi}{6}\)
बिंदु द्वितीय चतुर्थांश में है और संदर्भ कोण \(\frac{\pi}{6}\) है। इसलिए मुख्य कोण \(\frac{5\pi}{6}\) है। / The point is in the second quadrant and the reference angle is \(\frac{\pi}{6}\). Hence the principal angle is \(\frac{5\pi}{6}\).
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What is the principal angle between (0) and \(2\pi\) for \(-\frac{101\pi}{18}\)?
A. \(\frac{7\pi}{18}\)
\(-\frac{101\pi}{18}+6\pi=\frac{7\pi}{18}\)। परीक्षा में \(6\pi\) को \(\frac{108\pi}{18}\) लिखकर जोड़ना आसान होता है। / \(-\frac{101\pi}{18}+6\pi=\frac{7\pi}{18}\). In exams, writing \(6\pi\) as \(\frac{108\pi}{18}\) makes addition easy.
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What is the principal angle of \(-725^\circ\) in \(0^\circ\leq\theta<360^\circ\)?
D. \(355^\circ\)
\(-725^\circ+1080^\circ=355^\circ\)। परीक्षा में ऋणात्मक कोण में \(360^\circ\) के गुणज जोड़ते रहें। / \(-725^\circ+1080^\circ=355^\circ\). In exams, keep adding multiples of \(360^\circ\) to a negative angle.
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What is the principal angle between (0) and \(2\pi\) for \(-\frac{83\pi}{10}\)?
B. \(\frac{17\pi}{10}\)
\(-\frac{83\pi}{10}+10\pi=\frac{17\pi}{10}\)। परीक्षा में \(2\pi\) के बड़े गुणज जोड़कर कोण को दिए अंतराल में लाएं। / \(-\frac{83\pi}{10}+10\pi=\frac{17\pi}{10}\). In exams, add a suitable large multiple of \(2\pi\) to bring the angle into the given interval.
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If the principal angle of \(-\theta\) is \(110^\circ\), what is the principal angle of \(\theta\)?
D. \(250^\circ\)
\(-\theta\) का मुख्य कोण \(110^\circ\) है, इसलिए \(\theta\) का मुख्य कोण \(-110^\circ+360^\circ=250^\circ\) होगा। परीक्षा में संकेत बदलने पर \(360^\circ\) से समायोजन करें। / The principal angle of \(-\theta\) is \(110^\circ\), so the principal angle of \(\theta\) is \(-110^\circ+360^\circ=250^\circ\). In exams, adjust with \(360^\circ\) after changing the sign.
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What are the principal angle and quadrant of \(1245^\circ\)?
D. \(165^\circ\), दूसरा चतुर्थांश\(165^\circ\), second quadrant
\(1245^\circ-1080^\circ=165^\circ\), इसलिए कोण दूसरे चतुर्थांश में है। परीक्षा में पहले \(360^\circ\) के गुणज घटाएं। / \(1245^\circ-1080^\circ=165^\circ\), so the angle lies in the second quadrant. In exams, first subtract multiples 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 \(-\frac{7\pi}{6}\) 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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What will be the principal angle of \( -2215^\circ \) between \(0^\circ\) and \(360^\circ\)?
D. \(315^\circ\)
\( -2215^\circ+2520^\circ=305^\circ \) है? सही गणना में \( -2215^\circ+2520^\circ=305^\circ \) मिलता है। / \( -2215^\circ+2520^\circ=305^\circ \). Add a suitable multiple of \(360^\circ\) and then check the range.
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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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What will be the principal angle of \(1540^\circ\)?
C. \(100^\circ\)
\(1540^\circ-1440^\circ=100^\circ\) है। मुख्य कोण सामान्यतः \(0^\circ\) से \(360^\circ\) के बीच लिया जाता है। / \(1540^\circ-1440^\circ=100^\circ\). The principal angle is usually taken between \(0^\circ\) and \(360^\circ\).
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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 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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If an angle is \(370^\circ\), what is its principal angle between \(0^\circ\) and \(360^\circ\)?
D. \(10^\circ\)
\(370^\circ-360^\circ=10^\circ\) होता है। एक पूरा चक्कर घटाकर मुख्य कोण पाएं। / \(370^\circ-360^\circ=10^\circ\). Subtract one complete revolution to get the principal angle.
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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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