Trigonometric Identities Question 137
Question: If $ \tan \theta =-\frac{1}{\sqrt{10}} $ and $ \theta $ lies in the fourth quadrant, then $ \cos \theta = $
Options:
A) $ 1/\sqrt{11} $
B) $ -1/\sqrt{11} $
C) $ \sqrt{\frac{10}{11}} $
D) $ -\sqrt{\frac{10}{11}} $
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ \tan \theta =-\frac{1}{\sqrt{10}}, $ therefore $ \theta $ is in IV quadrant. So $ \cos \theta =+ve $ . Now $ 1+{{\tan }^{2}}\theta ={{\sec }^{2}}\theta \Rightarrow 1+\frac{1}{10}={{\sec }^{2}}\theta $
$ \Rightarrow {{\sec }^{2}}\theta =\frac{11}{10}\Rightarrow \cos \theta =\sqrt{( \frac{10}{11} )} $ .
BETA
