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

The Pythagorean identity connects $\sin\theta$ and $\cos\theta$ directly, and since $\theta$ is acute both ratios are positive.

Step 1 — apply the Pythagorean identity.

Step 2 — take the square root, choosing the sign. Since $\theta$ is acute (between $0°$ and $90°$), $\sin\theta$ is positive:

$\sin\theta = \sqrt{\frac{16}{25}} = \frac45$ …

Alternatively, treat $\cos\theta=\frac35$ as adjacent = 3, hypotenuse = 5 in a right triangle; then opposite $=\sqrt{5^2-3^2}=4$ by the Pythagorean theorem directly, giving the same $\si …

Forgetting to check whether $\theta$ is acute before choosing the sign of the square root is the main risk — for an obtuse $\theta$, $\sin\theta$ would still be positive but $\tan\thet …