If $\sin \theta =\frac{3}{5}$ and $\theta$ is an acute angle, find $\cos \theta$.

Step-by-step solution

1. Use the Pythagorean identity ${\sin }^2\theta +{\cos }^2\theta =1$.
2. Square the given sine value: $(\frac{3}{5}{)}^2=\frac{9}{25}$.
3. Substitute into the identity: $\frac{9}{25}+{\cos }^2\theta =1$.
4. Solve for ${\cos }^2\theta$: ${\cos }^2\theta =1-\frac{9}{25}=\frac{16}{25}$.
5. Since $\theta$ is acute, $\cos \theta$ is positive, so $\cos \theta =\sqrt{\frac{16}{25}}=\frac{4}{5}$.

Concept tested: Pythagorean identity for acute angles

Published 20 August 2026 · How this solution was prepared and checked