If $\sin heta = \frac{a}{b}$, then $\cos heta$ is equal to:

Question

If $\sin 	heta = \frac{a}{b}$, then $\cos 	heta$ is equal to:

Accepted Answer

Using the fundamental identity $\sin^2 	heta + \cos^2 	heta = 1$, we get $\cos^2 	heta = 1 - \sin^2 	heta$. Substituting $\sin 	heta = \frac{a}{b}$, we have $\cos^2 	heta = 1 - \frac{a^2}{b^2} = \frac{b^2 - a^2}{b^2}$. Taking square root on both sides, $\cos 	heta = \frac{\sqrt{b^2 - a^2}}{b}$.

Introduction to Trigonometry

❓ Sibling Questions in this Chapter