In a right triangle, if $\sin \theta$ = $\frac{3}{5}$, what is the value of $\cos \theta$?

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{4}$
• D. $\frac{5}{3}$

Answer: (B)

Verified step by step guidance

1. Identify the given information: \( \sin(\theta) = \frac{3}{5} \). This means in a right triangle, the ratio of the length of the side opposite angle \( \theta \) to the hypotenuse is \( \frac{3}{5} \).
2. Recall the Pythagorean identity relating sine and cosine: \( \sin^2(\theta) + \cos^2(\theta) = 1 \). This identity holds for any angle \( \theta \).
3. Substitute the given sine value into the identity: \( \left(\frac{3}{5}\right)^2 + \cos^2(\theta) = 1 \).
4. Calculate \( \left(\frac{3}{5}\right)^2 = \frac{9}{25} \), so the equation becomes \( \frac{9}{25} + \cos^2(\theta) = 1 \).
5. Solve for \( \cos^2(\theta) \) by subtracting \( \frac{9}{25} \) from both sides: \( \cos^2(\theta) = 1 - \frac{9}{25} = \frac{16}{25} \). Then take the positive square root (since cosine is positive in the context of a right triangle's acute angle): \( \cos(\theta) = \frac{4}{5} \).