Question

For any acute angle $\theta ,\sin (\pi +\theta )=$, $\cos (\pi +\theta )=$.

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

Answer 1

Answer: (A), (B)

$-\cos \theta$

Given an acute angle $\theta$ and we have to find the value of $\sin (\pi +\theta )\&\cos (\pi +\theta )$
Now, $\pi +\theta$ corresponds to angle in the 3rd quadrant, where both $\sin \&\cos$ are negative.
Now, the situation can be represented as:

Thus, equating we get:
$\cos (\pi +\theta )=-\cos \theta$
and $\sin (\pi +\theta )=-\sin \theta$