Question

If \( \sin \theta = \frac{a}{b} \), then the value of \( \cos \theta \) is:

• A. \( \frac{b}{\sqrt{b^2 - a^2}} \)
• B. \( \frac{\sqrt{b^2 - a^2}}{b} \)
• C. \( \frac{a}{\sqrt{b^2 - a^2}} \)
• D. \( \frac{b}{a} \)

Hint:

Use the identity: \[ \sin^2 \theta + \cos^2 \theta = 1 \] to find one trigonometric function from another.

Answer 1

The Correct Option is B

Using the Pythagorean identity:
\[ \sin^2 \theta + \cos^2 \theta = 1. \] \[ \left(\frac{a}{b}\right)^2 + \cos^2 \theta = 1. \] \[ \cos^2 \theta = 1 - \frac{a^2}{b^2}. \] \[ \cos \theta = \frac{\sqrt{b^2 - a^2}}{b}. \]