Question

If $\tan \theta$ = $\frac{6}{8}$ and $\theta$ is acute, what is the value of $\cos \theta$?

• A. $\frac{6}{10}$
• B. $\frac{8}{10}$
• C. $\frac{10}{10}$
• D. $\frac{5}{10}$

Answer 1

The correct option is B $\frac{8}{10}$

First use the identity: $1+{\tan }^2\theta ={\sec }^2\theta$
and substitute the value of $\tan \theta =\frac{6}{8}$

Therefore, $1+{\left(\frac{6}{8}\right)}^2={\sec }^2\theta$

$1+\sqrt{\frac{36}{64}}={\sec }^2\theta$

$\sec \theta =\sqrt{\frac{100}{64}}$

Taking square roots on both the sides, we get
$\sec \theta =\frac{10}{8}$

Now we know the value of $\sec \theta$, to find $\cos \theta$ we just take the reciprocal.

Therefore, $\cos \theta =\frac{8}{10}$

So, option $B$ is correct.