Trigonometric Equations Question 309
If $ \tan \theta =-\frac{1}{\sqrt{3}} $ and $ \sin \theta =\frac{1}{2} $ , then the principal value of $ \theta $ will be
[MP PET 1983, 84]
Options:
A) $ \frac{\pi }{6} $
B) $ \frac{5\pi }{6} $
C) $ \frac{7\pi }{6} $
D) $ -\frac{\pi }{6} $
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Answer:
Correct Answer: B
Solution:
- $ \tan \theta =\frac{-1}{\sqrt{3}}=\tan ( \pi -\frac{\pi }{6} ) $ , $ \sin \theta =\frac{1}{2}=\sin ( \pi -\frac{\pi }{6} ) $ and $ \cos \theta =\frac{-\sqrt{3}}{2} $ = $ \cos ( \pi -\frac{\pi }{6} ) $ Hence principal value is $ \theta =\frac{5\pi }{6} $ .
BETA
