Question
If $\cos \theta=\frac{24}{25}$, then $\sin \theta=?$
✓
Answer
$\cos \theta=\frac{24}{25}$
We know that,
$ \sin ^2 \theta+\cos ^2 \theta=1$
$\therefore \sin ^2 \theta+\left(\frac{24}{25}\right)^2=1$
$\therefore \sin ^2 \theta+\frac{576}{625}=1$
$\therefore \sin ^2 \theta=1-\frac{576}{625}$
$\therefore \sin ^2 \theta=\frac{625-576}{625}$
$\therefore \sin ^2 \theta=\frac{49}{625}$
$\therefore \sin ^2 \theta=\frac{7}{25} \quad \ldots . . .[\text { Taking square root of both sides] } $
We know that,
$ \sin ^2 \theta+\cos ^2 \theta=1$
$\therefore \sin ^2 \theta+\left(\frac{24}{25}\right)^2=1$
$\therefore \sin ^2 \theta+\frac{576}{625}=1$
$\therefore \sin ^2 \theta=1-\frac{576}{625}$
$\therefore \sin ^2 \theta=\frac{625-576}{625}$
$\therefore \sin ^2 \theta=\frac{49}{625}$
$\therefore \sin ^2 \theta=\frac{7}{25} \quad \ldots . . .[\text { Taking square root of both sides] } $
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