Question

If $\tan \theta =\frac{4}{3}$, what is the value of $\cos \theta$?

• A. 0.6

Answer 1

The correct option is A 0.6
We know
${\sec }^2\theta -{\tan }^2\theta =1\Rightarrow {\sec }^2\theta =1+{\tan }^2\theta \Rightarrow \sec \theta =\sqrt{1+{\tan }^2\theta }\Rightarrow \sec \theta =\sqrt{1+(\frac{4}{3}{)}^2}\Rightarrow \sec \theta =\sqrt{\frac{9+16}{9}}\Rightarrow \sec \theta =\sqrt{\frac{25}{9}}\Rightarrow \sec \theta =\frac{5}{3}\Rightarrow \cos \theta =\frac{3}{5}=0.6$