Question

If $\cos \theta =\frac{8}{10}$ and $\theta$ is acute, what is the value of $\text{cosec}\theta$?

• A. $\frac{10}{6}$
• B. $\frac{8}{10}$
• C. $\frac{1}{8}$
• D. $\frac{10}{7}$

Answer 1

Answer: (A)

$\frac{10}{6}$

First use the identity: ${\sin }^2\theta +{\cos }^2\theta =1$ and substitute the value of $\cos \theta =\frac{8}{10}$

Therefore, ${\left(\frac{8}{10}\right)}^2+{\sin }^2\theta =1$

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

Squaring on both the sides, we get
${\sin }^2\theta =\sqrt{\frac{36}{100}}=\frac{6}{10}$

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

Therefore, $\text{cosec}\theta =\frac{10}{6}$

So, option $A$ is correct.