Trigonometric Equations Question 59
Question: If $ \cos \theta =\frac{-1}{2} $ and $ 0^{o}<\theta <360^{o} $ , then the values of $ \theta $ are
[Karnataka CET 2001]
Options:
A) $ 120^{o} $ and $ 300^{o} $
B) $ 60^{o} $ and $ 120^{o} $
C) $ 120^{o} $ and $ 240^{o} $
D) $ 60^{o} $ and $ 240^{o} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ \cos \theta =\frac{-1}{2} $ and $ 0^{o}<\theta <360^{o} $ . We know that $ \cos 60^{o}=\frac{1}{2} $ and $ \cos (180^{o}-60^{o}) $ $ =-\cos 60^{o}=-\frac{1}{2} $ or $ \cos 120^{o}=-\frac{1}{2} $ . Similarly $ \cos (180^{o}+60^{o}) $ $ =-\cos 60^{o}=-\frac{1}{2} $ or $ \cos 240^{o}=-\frac{1}{2}. $ Therefore $ \theta =120^{o} $ and $ 240^{o} $ .
BETA
