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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 2 of 61
Marks: +1, -0
Find the degree measures corresponding to the following radian measures (Use π = 22/7)
(i) 1116\frac{11}{16}
(ii) - 4
(iii) 5π3\frac{5\pi}{3}
(iv) 7π6\frac{7\pi}{6}
Solution:  
We have, π Radians = 180°
⇒ 1 radian = (180π)\left(\frac{180}{\pi}\right)^{\circ}
(i) 1116\frac{11}{16} radians = (1116×180π)\left(\frac{11}{16} \times \frac{180}{\pi}\right)^{\circ} = (3158)\left(\frac{315}{8}\right)^{\circ} = 39° 22' 30" [Since 1° = 60']
(ii) - 4 radians = (4×180π)\left(\frac{-4 \times 180}{\pi}\right)^{\circ} = - 229° 5' 27"
(iii) 5π3\frac{5\pi}{3} radians = (53×180π)\left(\frac{5}{3} \times \frac{180}{\pi}\right)^{\circ} = 300°
(iv) 7π6\frac{7\pi}{6} radians = (7π6×180π)\left(\frac{7\pi}{6} \times \frac{180}{\pi}\right)^{\circ} = 210°
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