Question

If $\sin \theta =\frac{7}{25}$, where $\theta$ is an acute, find the value of $\cos \theta$ using identity.

Answer 1

Given, $\sin \theta =\frac{7}{25}$

$\therefore \cos \theta =\sqrt{1-{\sin }^2\theta }$ [$\because {\sin }^{2}A+{\cos }^{2}A=1$]

$\Rightarrow \cos \theta =\sqrt{1-\frac{49}{625}}$

$\Rightarrow \cos \theta =\sqrt{\frac{576}{625}}$

$\Rightarrow \cos \theta =\sqrt{\frac{24\times 24}{25\times 25}}$

$\Rightarrow \cos \theta =\frac{24}{25}$