Question

Find the value of $\tan \theta$ given that $\cos \theta =0.75$

• A. $0.60$
• B. $0.67$
• C. $0.75$
• D. $0.88$
• E. $1.33$

Answer 1

The correct option is D $0.88$

Given, $\cos \theta =0.75$

$\Rightarrow \sec \theta =\frac{1}{\cos \theta }=\frac{1}{0.75}=\frac{4}{3}$
We now that $\tan \theta =\sqrt{{\sec }^2\theta -1}$

$=\sqrt{{\left(\frac{4}{3}\right)}^2-1}$

$=\sqrt{0.777}$

$=0.88$