Question

If $sin\theta =\frac{20}{29}$, find $cos\theta$.

• A. $\frac{9}{29}$
• B. $1$
• C. $\frac{20}{29}$
• D. $\frac{21}{29}$

Answer 1

The correct option is D $\frac{21}{29}$

Given,
$sin\theta =\frac{20}{29}$

We know that,
$si{n}^2\theta +co{s}^2\theta =1$
$co{s}^2\theta =1-si{n}^2\theta$

Now,
$co{s}^2\theta =1-(\frac{20}{29}{)}^2$
$co{s}^2\theta =1-\left(\frac{400}{841}\right)$
$co{s}^2\theta =\frac{441}{841}$
$cos\theta =\left(\frac{21}{29}\right)$

Hence, $cos\theta =\left(\frac{21}{29}\right)$