Question

If $\sin \theta =\frac{6}{10}$ and $\theta$ is acute, what is the value of $\sec \theta$?

• A. $\frac{10}{8}$
• B. $\frac{8}{10}$
• C. $\frac{1}{8}$
• D. $\frac{10}{7}$

Answer 1

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

First use the identity: ${\sin }^2\theta +{\cos }^2\theta =1$ and substitute the value of $\sin \theta =\frac{6}{10}$

Therefore, ${\left(\frac{6}{10}\right)}^2+{\cos }^2\theta =1$

${\cos }^2\theta =1-\frac{36}{100}=\frac{64}{100}$

Square root on both the sides, we get
${\cos }^{}\theta =\sqrt{\frac{64}{100}}=\frac{8}{10}$

Now we know the value of ${\cos }^2\theta$, to find ${\sec }^2\theta$ we just take the reciprocal.

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

So, option $A$ is correct.