Question

$cos(\frac{3\pi }{2}+\theta )$ =...............

• A. - cos $\theta$
• B. cos $\theta$
• C. sin $\theta$
• D. - sin $\theta$

Answer 1

The correct option is C sin $\theta$

$\cos (\frac{3\pi }{2}+\theta )$

$=\cos (\pi +(\frac{\pi }{2}+\theta ))$ since $\pi +\theta$ is in third quadrant cosine is negative.

$=-\cos (\frac{\pi }{2}+\theta )$ since $\frac{\pi }{2}+\theta$ is in second quadrant cosine is negative.

$=\sin \theta$