Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है
A. \( \frac{\pi}{10} \) रेडियन/\( \frac{\pi}{10} \) radians
Step 1
Concept
\(18^\circ=\frac{18\pi}{180}=\frac{\pi}{10}\). Multiply by \( \frac{\pi}{180} \) to convert degrees to radians.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{\pi}{10} \) रेडियन / \( \frac{\pi}{10} \) radians. \(18^\circ=\frac{18\pi}{180}=\frac{\pi}{10}\). Multiply by \( \frac{\pi}{180} \) to convert degrees to radians.
Step 3
Exam Tip
\(18^\circ=\frac{18\pi}{180}=\frac{\pi}{10}\) है। डिग्री से रेडियन में बदलते समय \( \frac{\pi}{180} \) से गुणा करें।
B. \( \frac{3\pi}{10} \) रेडियन/\( \frac{3\pi}{10} \) radians
Step 1
Concept
\(54^\circ=\frac{54\pi}{180}=\frac{3\pi}{10}\). It is important to write the fraction in simplest form.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{3\pi}{10} \) रेडियन / \( \frac{3\pi}{10} \) radians. \(54^\circ=\frac{54\pi}{180}=\frac{3\pi}{10}\). It is important to write the fraction in simplest form.
Step 3
Exam Tip
\(54^\circ=\frac{54\pi}{180}=\frac{3\pi}{10}\) होता है। भिन्न को सबसे सरल रूप में लिखना जरूरी है।
C. \( \frac{7\pi}{10} \) रेडियन/\( \frac{7\pi}{10} \) radians
Step 1
Concept
\(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}\). Dividing by (18) makes simplification faster.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{7\pi}{10} \) रेडियन / \( \frac{7\pi}{10} \) radians. \(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}\). Dividing by (18) makes simplification faster.
Step 3
Exam Tip
\(126^\circ=\frac{126\pi}{180}=\frac{7\pi}{10}\) है। (18) से भाग देकर सरलीकरण तेज होता है।
D. \( \frac{11\pi}{10} \) रेडियन/\( \frac{11\pi}{10} \) radians
Step 1
Concept
\(198^\circ=\frac{198\pi}{180}=\frac{11\pi}{10}\). An angle slightly greater than \(180^\circ\) gives a radian value slightly greater than \(\pi\).
Step 2
Why this answer is correct
The correct answer is D. \( \frac{11\pi}{10} \) रेडियन / \( \frac{11\pi}{10} \) radians. \(198^\circ=\frac{198\pi}{180}=\frac{11\pi}{10}\). An angle slightly greater than \(180^\circ\) gives a radian value slightly greater than \(\pi\).
Step 3
Exam Tip
\(198^\circ=\frac{198\pi}{180}=\frac{11\pi}{10}\) है। \(180^\circ\) से थोड़ा बड़ा कोण \(\pi\) से थोड़ा बड़ा रेडियन देता है।
A. \( \frac{7\pi}{5} \) रेडियन/\( \frac{7\pi}{5} \) radians
Step 1
Concept
\(252^\circ=\frac{252\pi}{180}=\frac{7\pi}{5}\). Divide the degree measure by (180) and attach \(\pi\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7\pi}{5} \) रेडियन / \( \frac{7\pi}{5} \) radians. \(252^\circ=\frac{252\pi}{180}=\frac{7\pi}{5}\). Divide the degree measure by (180) and attach \(\pi\).
Step 3
Exam Tip
\(252^\circ=\frac{252\pi}{180}=\frac{7\pi}{5}\) होता है। डिग्री को (180) से भाग देकर \(\pi\) लगाएं।
B. \(-\frac{7\pi}{4}\) रेडियन/\(-\frac{7\pi}{4}\) radians
Step 1
Concept
\(-315^\circ=\frac{-315\pi}{180}=-\frac{7\pi}{4}\). Keep the negative sign until the final answer.
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{7\pi}{4}\) रेडियन / \(-\frac{7\pi}{4}\) radians. \(-315^\circ=\frac{-315\pi}{180}=-\frac{7\pi}{4}\). Keep the negative sign until the final answer.
Step 3
Exam Tip
\(-315^\circ=\frac{-315\pi}{180}=-\frac{7\pi}{4}\) है। ऋणात्मक चिह्न को अंतिम उत्तर तक बनाए रखें।
C. \( \frac{3\pi}{16} \) रेडियन/\( \frac{3\pi}{16} \) radians
Step 1
Concept
\(33^\circ45'=33.75^\circ=\frac{135^\circ}{4}\) and the radian value is \( \frac{3\pi}{16} \). Convert minutes into degrees first.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{3\pi}{16} \) रेडियन / \( \frac{3\pi}{16} \) radians. \(33^\circ45'=33.75^\circ=\frac{135^\circ}{4}\) and the radian value is \( \frac{3\pi}{16} \). Convert minutes into degrees first.
Step 3
Exam Tip
\(33^\circ45'=33.75^\circ=\frac{135^\circ}{4}\) और रेडियन मान \( \frac{3\pi}{16} \) है। पहले मिनट को डिग्री में बदलें।
D. \( \frac{\pi}{80} \) रेडियन/\( \frac{\pi}{80} \) radians
Step 1
Concept
\(2^\circ15'=2.25^\circ\) and \(2.25^\circ\times \frac{\pi}{180}=\frac{\pi}{80}\). Convert small degree measures carefully into decimals.
Step 2
Why this answer is correct
The correct answer is D. \( \frac{\pi}{80} \) रेडियन / \( \frac{\pi}{80} \) radians. \(2^\circ15'=2.25^\circ\) and \(2.25^\circ\times \frac{\pi}{180}=\frac{\pi}{80}\). Convert small degree measures carefully into decimals.
Step 3
Exam Tip
\(2^\circ15'=2.25^\circ\) और \(2.25^\circ\times \frac{\pi}{180}=\frac{\pi}{80}\) है। छोटी डिग्री में दशमलव परिवर्तन सावधानी से करें।
\( \frac{13\pi}{18}\times\frac{180^\circ}{\pi}=130^\circ\). If the denominator is (18), take \(180^\circ\div18=10^\circ\).
Step 2
Why this answer is correct
The correct answer is B. \(130^\circ\). \( \frac{13\pi}{18}\times\frac{180^\circ}{\pi}=130^\circ\). If the denominator is (18), take \(180^\circ\div18=10^\circ\).
Step 3
Exam Tip
\( \frac{13\pi}{18}\times\frac{180^\circ}{\pi}=130^\circ\) होता है। हर (18) हो तो \(180^\circ\div18=10^\circ\) लें।
\( \frac{11\pi}{15}\times\frac{180^\circ}{\pi}=132^\circ\). Calculate \(180^\circ\div15=12^\circ\) and multiply.
Step 2
Why this answer is correct
The correct answer is C. \(132^\circ\). \( \frac{11\pi}{15}\times\frac{180^\circ}{\pi}=132^\circ\). Calculate \(180^\circ\div15=12^\circ\) and multiply.
Step 3
Exam Tip
\( \frac{11\pi}{15}\times\frac{180^\circ}{\pi}=132^\circ\) है। \(180^\circ\div15=12^\circ\) करके गुणा करें।
\(-\frac{9\pi}{8}\times\frac{180^\circ}{\pi}=-202.5^\circ\). The negative sign in radians remains in degrees.
Step 2
Why this answer is correct
The correct answer is D. \(-202.5^\circ\). \(-\frac{9\pi}{8}\times\frac{180^\circ}{\pi}=-202.5^\circ\). The negative sign in radians remains in degrees.
Step 3
Exam Tip
\(-\frac{9\pi}{8}\times\frac{180^\circ}{\pi}=-202.5^\circ\) है। ऋणात्मक रेडियन का चिह्न डिग्री में भी रहता है।
\(-\frac{41\pi}{10}+\frac{60\pi}{10}=\frac{19\pi}{10}\). Add enough multiples of \(2\pi\) to a negative angle.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{19\pi}{10} \). \(-\frac{41\pi}{10}+\frac{60\pi}{10}=\frac{19\pi}{10}\). Add enough multiples of \(2\pi\) to a negative angle.
Step 3
Exam Tip
\(-\frac{41\pi}{10}+\frac{60\pi}{10}=\frac{19\pi}{10}\) है। ऋणात्मक कोण में \(2\pi\) के पर्याप्त गुणज जोड़ें।
\(-\frac{29\pi}{5}+\frac{30\pi}{5}=\frac{\pi}{5}\). Keeping the same denominator makes radian calculation easy.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{\pi}{5} \). \(-\frac{29\pi}{5}+\frac{30\pi}{5}=\frac{\pi}{5}\). Keeping the same denominator makes radian calculation easy.
Step 3
Exam Tip
\(-\frac{29\pi}{5}+\frac{30\pi}{5}=\frac{\pi}{5}\) है। हर समान रखने से रेडियन गणना सरल होती है।
\(1485^\circ-45^\circ=1440^\circ=4\times360^\circ\), so they are coterminal. If the difference is a multiple of \(360^\circ\), consider them coterminal.
Step 2
Why this answer is correct
The correct answer is D. वे सहसमापी कोण हैं / They are coterminal angles. \(1485^\circ-45^\circ=1440^\circ=4\times360^\circ\), so they are coterminal. If the difference is a multiple of \(360^\circ\), consider them coterminal.
Step 3
Exam Tip
\(1485^\circ-45^\circ=1440^\circ=4\times360^\circ\) इसलिए वे सहसमापी हैं। अंतर \(360^\circ\) का गुणज हो तो सहसमापी मानें।
\(-640^\circ+720^\circ=80^\circ\), and \(80^\circ\) lies in the first quadrant. First convert a negative angle into a positive coterminal angle.
Step 2
Why this answer is correct
The correct answer is A. प्रथम चतुर्थांश / First quadrant. \(-640^\circ+720^\circ=80^\circ\), and \(80^\circ\) lies in the first quadrant. First convert a negative angle into a positive coterminal angle.
Step 3
Exam Tip
\(-640^\circ+720^\circ=80^\circ\) है और \(80^\circ\) प्रथम चतुर्थांश में है। ऋणात्मक कोण को पहले धनात्मक सहसमापी कोण में बदलें।
\( \frac{3\pi}{2}<\frac{23\pi}{14}<2\pi \), so it lies in the fourth quadrant. Compare radian limits with a common denominator.
Step 2
Why this answer is correct
The correct answer is D. चतुर्थ चतुर्थांश / Fourth quadrant. \( \frac{3\pi}{2}<\frac{23\pi}{14}<2\pi \), so it lies in the fourth quadrant. Compare radian limits with a common denominator.
Step 3
Exam Tip
\( \frac{3\pi}{2}<\frac{23\pi}{14}<2\pi \) है इसलिए यह चतुर्थ चतुर्थांश में है। रेडियन सीमाओं की तुलना समान हर से करें।
\( \frac{\pi}{2}<\frac{6\pi}{11}<\pi \), so the terminal side lies in the second quadrant. The interval between \( \frac{\pi}{2} \) and \( \pi \) is the second quadrant.
Step 2
Why this answer is correct
The correct answer is B. द्वितीय चतुर्थांश / Second quadrant. \( \frac{\pi}{2}<\frac{6\pi}{11}<\pi \), so the terminal side lies in the second quadrant. The interval between \( \frac{\pi}{2} \) and \( \pi \) is the second quadrant.
Step 3
Exam Tip
\( \frac{\pi}{2}<\frac{6\pi}{11}<\pi \) है इसलिए अंतिम भुजा द्वितीय चतुर्थांश में है। \( \frac{\pi}{2} \) और \( \pi \) के बीच दूसरा चतुर्थांश होता है।
\( \pi<\frac{15\pi}{11}<\frac{3\pi}{2} \), so it lies in the third quadrant. After \( \pi \) and before \( \frac{3\pi}{2} \) is the third quadrant.
Step 2
Why this answer is correct
The correct answer is C. तृतीय चतुर्थांश / Third quadrant. \( \pi<\frac{15\pi}{11}<\frac{3\pi}{2} \), so it lies in the third quadrant. After \( \pi \) and before \( \frac{3\pi}{2} \) is the third quadrant.
Step 3
Exam Tip
\( \pi<\frac{15\pi}{11}<\frac{3\pi}{2} \) है इसलिए यह तृतीय चतुर्थांश में आता है। \( \pi \) के बाद और \( \frac{3\pi}{2} \) से पहले तीसरा चतुर्थांश होता है।
\( -\frac{5\pi}{8}+2\pi=\frac{11\pi}{8} \), and it lies in the third quadrant. Add \(2\pi\) to a negative radian angle to check its position.
Step 2
Why this answer is correct
The correct answer is C. तृतीय चतुर्थांश / Third quadrant. \( -\frac{5\pi}{8}+2\pi=\frac{11\pi}{8} \), and it lies in the third quadrant. Add \(2\pi\) to a negative radian angle to check its position.
Step 3
Exam Tip
\( -\frac{5\pi}{8}+2\pi=\frac{11\pi}{8} \) है और यह तृतीय चतुर्थांश में है। ऋणात्मक रेडियन कोण में \(2\pi\) जोड़कर स्थिति देखें।
\(30'=\frac{30}{60}^\circ=0.5^\circ\), so the value is \(72.5^\circ\). Do not write minutes directly as decimals.
Step 2
Why this answer is correct
The correct answer is B. \(72.5^\circ\). \(30'=\frac{30}{60}^\circ=0.5^\circ\), so the value is \(72.5^\circ\). Do not write minutes directly as decimals.
Step 3
Exam Tip
\(30'=\frac{30}{60}^\circ=0.5^\circ\) इसलिए मान \(72.5^\circ\) है। मिनट को दशमलव में सीधे न लिखें।
\(0.125^\circ\times60'=7.5'\), and \(0.5'\times60''=30''\). Convert the decimal part step by step into minutes and seconds.
Step 2
Why this answer is correct
The correct answer is A. \(41^\circ 7'30''\). \(0.125^\circ\times60'=7.5'\), and \(0.5'\times60''=30''\). Convert the decimal part step by step into minutes and seconds.
Step 3
Exam Tip
\(0.125^\circ\times60'=7.5'\) और \(0.5'\times60''=30''\) है। दशमलव भाग को क्रम से मिनट और सेकंड में बदलें।
B. \( \frac{2\pi}{3} \) रेडियन/\( \frac{2\pi}{3} \) radians
Step 1
Concept
\( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} \). Use \( \theta=\frac{s}{r} \) to find the angle from arc length.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{2\pi}{3} \) रेडियन / \( \frac{2\pi}{3} \) radians. \( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} \). Use \( \theta=\frac{s}{r} \) to find the angle from arc length.
Step 3
Exam Tip
\( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} \) है। चाप लंबाई से कोण निकालते समय \( \theta=\frac{s}{r} \) लगाएं।
\(s=r\theta=16\times\frac{5\pi}{8}=10\pi\) cm. When the angle is in radians, \(s=r\theta\) applies directly.
Step 2
Why this answer is correct
The correct answer is C. \(10\pi\) सेमी / \(10\pi\) cm. \(s=r\theta=16\times\frac{5\pi}{8}=10\pi\) cm. When the angle is in radians, \(s=r\theta\) applies directly.
Step 3
Exam Tip
\(s=r\theta=16\times\frac{5\pi}{8}=10\pi\) सेमी है। कोण रेडियन में हो तो \(s=r\theta\) सीधे लागू होता है।
\(75^\circ=\frac{5\pi}{12}\), and \(s=24\times\frac{5\pi}{12}=10\pi\) cm. Convert degrees to radians before finding the arc.
Step 2
Why this answer is correct
The correct answer is B. \(10\pi\) सेमी / \(10\pi\) cm. \(75^\circ=\frac{5\pi}{12}\), and \(s=24\times\frac{5\pi}{12}=10\pi\) cm. Convert degrees to radians before finding the arc.
Step 3
Exam Tip
\(75^\circ=\frac{5\pi}{12}\) और \(s=24\times\frac{5\pi}{12}=10\pi\) सेमी है। चाप निकालने से पहले डिग्री को रेडियन में बदलें।
Area is \( \frac{1}{2}r^2\theta=\frac{1}{2}\times196\times\frac{5\pi}{7}=70\pi \). Use this formula directly with a radian angle.
Step 2
Why this answer is correct
The correct answer is C. \(70\pi\) वर्ग सेमी / \(70\pi\) square cm. Area is \( \frac{1}{2}r^2\theta=\frac{1}{2}\times196\times\frac{5\pi}{7}=70\pi \). Use this formula directly with a radian angle.
Step 3
Exam Tip
क्षेत्रफल \( \frac{1}{2}r^2\theta=\frac{1}{2}\times196\times\frac{5\pi}{7}=70\pi \) है। रेडियन कोण के साथ यह सूत्र सीधे लगाएं।
\(120^\circ=\frac{2\pi}{3}\), and area is \( \frac{1}{2}\times81\times\frac{2\pi}{3}=27\pi \). Convert the degree angle into radians first.
Step 2
Why this answer is correct
The correct answer is B. \(27\pi\) वर्ग सेमी / \(27\pi\) square cm. \(120^\circ=\frac{2\pi}{3}\), and area is \( \frac{1}{2}\times81\times\frac{2\pi}{3}=27\pi \). Convert the degree angle into radians first.
Step 3
Exam Tip
\(120^\circ=\frac{2\pi}{3}\) और क्षेत्रफल \( \frac{1}{2}\times81\times\frac{2\pi}{3}=27\pi \) है। डिग्री कोण को पहले रेडियन में बदलें।
From \(54=\frac{1}{2}\times36\times\theta\), \( \theta=3 \) radians. Isolate the unknown angle in the sector area formula.
Step 2
Why this answer is correct
The correct answer is B. (3) रेडियन / (3) radians. From \(54=\frac{1}{2}\times36\times\theta\), \( \theta=3 \) radians. Isolate the unknown angle in the sector area formula.
Step 3
Exam Tip
\(54=\frac{1}{2}\times36\times\theta\) से \( \theta=3 \) रेडियन है। क्षेत्रफल सूत्र में अज्ञात कोण को अलग करें।
Sector area is \( \frac{1}{2}rs \), so \(150=\frac{1}{2}\times r\times20\) gives (r=15). When arc length is given, \( \frac{1}{2}rs \) is useful.
Step 2
Why this answer is correct
The correct answer is C. (15) सेमी / (15) cm. Sector area is \( \frac{1}{2}rs \), so \(150=\frac{1}{2}\times r\times20\) gives (r=15). When arc length is given, \( \frac{1}{2}rs \) is useful.
Step 3
Exam Tip
त्रिज्यखंड क्षेत्रफल \( \frac{1}{2}rs \) है इसलिए \(150=\frac{1}{2}\times r\times20\) से (r=15) है। चाप दिया हो तो \( \frac{1}{2}rs \) उपयोगी है।
\( \frac{3\pi}{5} \) lies in the second quadrant, and the reference angle is \( \pi-\frac{3\pi}{5}=\frac{2\pi}{5} \). In the second quadrant use \( \pi-\theta \).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{2\pi}{5} \). \( \frac{3\pi}{5} \) lies in the second quadrant, and the reference angle is \( \pi-\frac{3\pi}{5}=\frac{2\pi}{5} \). In the second quadrant use \( \pi-\theta \).
Step 3
Exam Tip
\( \frac{3\pi}{5} \) द्वितीय चतुर्थांश में है और संदर्भ कोण \( \pi-\frac{3\pi}{5}=\frac{2\pi}{5} \) है। द्वितीय चतुर्थांश में \( \pi-\theta \) लें।
\( \frac{8\pi}{7} \) lies in the third quadrant, and \( \frac{8\pi}{7}-\pi=\frac{\pi}{7} \). In the third quadrant use \( \theta-\pi \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{\pi}{7} \). \( \frac{8\pi}{7} \) lies in the third quadrant, and \( \frac{8\pi}{7}-\pi=\frac{\pi}{7} \). In the third quadrant use \( \theta-\pi \).
Step 3
Exam Tip
\( \frac{8\pi}{7} \) तृतीय चतुर्थांश में है और \( \frac{8\pi}{7}-\pi=\frac{\pi}{7} \) है। तृतीय चतुर्थांश में \( \theta-\pi \) प्रयोग करें।
\( \frac{13\pi}{6}-2\pi=\frac{\pi}{6} \), and it is in the first quadrant. First find the principal angle and then the reference angle.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{\pi}{6} \). \( \frac{13\pi}{6}-2\pi=\frac{\pi}{6} \), and it is in the first quadrant. First find the principal angle and then the reference angle.
Step 3
Exam Tip
\( \frac{13\pi}{6}-2\pi=\frac{\pi}{6} \) है और यह प्रथम चतुर्थांश में है। पहले मुख्य कोण फिर संदर्भ कोण निकालें।
\(300^\circ\) lies in the fourth quadrant, and \(360^\circ-300^\circ=60^\circ\). In the fourth quadrant use \(360^\circ-\theta\).
Step 2
Why this answer is correct
The correct answer is C. \(60^\circ\). \(300^\circ\) lies in the fourth quadrant, and \(360^\circ-300^\circ=60^\circ\). In the fourth quadrant use \(360^\circ-\theta\).
Step 3
Exam Tip
\(300^\circ\) चतुर्थ चतुर्थांश में है और \(360^\circ-300^\circ=60^\circ\) है। चतुर्थ चतुर्थांश में \(360^\circ-\theta\) करें।
\(240^\circ\) lies in the third quadrant, and \(240^\circ-180^\circ=60^\circ\). In the third quadrant subtract \(180^\circ\).
Step 2
Why this answer is correct
The correct answer is C. \(60^\circ\). \(240^\circ\) lies in the third quadrant, and \(240^\circ-180^\circ=60^\circ\). In the third quadrant subtract \(180^\circ\).
Step 3
Exam Tip
\(240^\circ\) तृतीय चतुर्थांश में है और \(240^\circ-180^\circ=60^\circ\) है। तृतीय चतुर्थांश में \(180^\circ\) घटाएं।
\(720^\circ=2\times360^\circ\), so its terminal side lies on the positive (x)-axis. Multiples of \(360^\circ\) return to this axis.
Step 2
Why this answer is correct
The correct answer is B. \(720^\circ\). \(720^\circ=2\times360^\circ\), so its terminal side lies on the positive (x)-axis. Multiples of \(360^\circ\) return to this axis.
Step 3
Exam Tip
\(720^\circ=2\times360^\circ\) है इसलिए अंतिम भुजा धनात्मक (x)-अक्ष पर होगी। \(360^\circ\) के गुणज इसी अक्ष पर लौटते हैं।
\(630^\circ-360^\circ=270^\circ\), and \(270^\circ\) lies on the negative (y)-axis. First find the coterminal angle.
Step 2
Why this answer is correct
The correct answer is B. \(630^\circ\). \(630^\circ-360^\circ=270^\circ\), and \(270^\circ\) lies on the negative (y)-axis. First find the coterminal angle.
Step 3
Exam Tip
\(630^\circ-360^\circ=270^\circ\) है और \(270^\circ\) ऋणात्मक (y)-अक्ष पर होता है। पहले सहसमापी कोण निकालें।
\( \frac{15\pi}{2}-6\pi=\frac{3\pi}{2} \), and \( \frac{3\pi}{2} \) lies on the negative (y)-axis. Subtract multiples of \(2\pi\) to identify the axis.
Step 2
Why this answer is correct
The correct answer is D. ऋणात्मक (y)-अक्ष / Negative (y)-axis. \( \frac{15\pi}{2}-6\pi=\frac{3\pi}{2} \), and \( \frac{3\pi}{2} \) lies on the negative (y)-axis. Subtract multiples of \(2\pi\) to identify the axis.
Step 3
Exam Tip
\( \frac{15\pi}{2}-6\pi=\frac{3\pi}{2} \) है और \( \frac{3\pi}{2} \) ऋणात्मक (y)-अक्ष पर है। \(2\pi\) के गुणज घटाकर अक्ष पहचानें।
\(1080^\circ=3\times360^\circ\), so such angles are coterminal. If the difference is a multiple of \(360^\circ\), the terminal side is the same.
Step 2
Why this answer is correct
The correct answer is C. वे सहसमापी होते हैं / They are coterminal. \(1080^\circ=3\times360^\circ\), so such angles are coterminal. If the difference is a multiple of \(360^\circ\), the terminal side is the same.
Step 3
Exam Tip
\(1080^\circ=3\times360^\circ\) है इसलिए ऐसे कोण सहसमापी होते हैं। अंतर \(360^\circ\) का गुणज हो तो अंतिम भुजा समान होती है।
