Question
If $\sin \theta=\frac{20}{29}$ then find $\cos \theta$
✓
Answer
Method I
We have
$
\sin ^2 \theta+\cos ^2 \theta=1
$
$
\begin{array}{c}
\left(\frac{20}{29}\right)^2+\cos ^2 \theta=1 \\
\frac{400}{841}+\cos ^2 \theta=1 \\
\cos ^2 \theta=1-\frac{400}{841} \\
=\frac{441}{841}
\end{array}
$
Taking square root of both sides.
$
\cos \theta=\frac{21}{29}
$
We have
$
\sin ^2 \theta+\cos ^2 \theta=1
$
$
\begin{array}{c}
\left(\frac{20}{29}\right)^2+\cos ^2 \theta=1 \\
\frac{400}{841}+\cos ^2 \theta=1 \\
\cos ^2 \theta=1-\frac{400}{841} \\
=\frac{441}{841}
\end{array}
$
Taking square root of both sides.
$
\cos \theta=\frac{21}{29}
$
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