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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 1 of 61
Marks: +1, -0
Find the radian measures corresponding to the following degree measures :
(i) 25°
(ii) –47°30’
(iii) 240°
(iv) 520°
Solution:  
We have, 180° = π Radians
∴ 1° = (π180)\left(\frac{\pi}{180}\right) radians
(i) 25° = (π180×25)\left(\frac{\pi}{180} \times 25\right) radians = 5π6\frac{5\pi}{6} radians
(ii) As we know, 30' = (3060)\left(\frac{30}{60}\right)^{\circ} = (12)\left(\frac{1}{2}\right)^{\circ}
∴ - 47° 30' = - (4712)\left(47\frac{1}{2}\right)^{\circ} = - (952)\left(\frac{95}{2}\right)^{\circ}
⇒ - (952)\left(\frac{95}{2}\right)^{\circ} = - (952×π180)\left(\frac{95}{2} \times \frac{\pi}{180}\right) radians = 19π72\frac{-19\pi}{72} radians
(iii) 240° = (π180×240)\left(\frac{\pi}{180} \times 240\right) radians = 4π3\frac{4\pi}{3} radians
(iv) 520° = (π180×520)\left(\frac{\pi}{180} \times 520\right) radians = 26π9\frac{26\pi}{9} radians
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