which expression is equivalent to cos(π/2 + r) for all values of r?\no sin(r)\no cos(r)\no -sin(r)\no -cos(r)
which expression is equivalent to cos(π/2 + r) for all values of r?\no sin(r)\no cos(r)\no -sin(r)\no -cos(r)
Answer
Explanation:
Step1: Use the cosine - addition formula
The cosine - addition formula is $\cos(A + B)=\cos A\cos B-\sin A\sin B$. Here, $A=\frac{\pi}{2}$ and $B = r$. So, $\cos(\frac{\pi}{2}+r)=\cos\frac{\pi}{2}\cos r-\sin\frac{\pi}{2}\sin r$.
Step2: Evaluate trigonometric values
We know that $\cos\frac{\pi}{2}=0$ and $\sin\frac{\pi}{2}=1$. Substituting these values into the above - expression, we get $0\times\cos r - 1\times\sin r=-\sin r$.
Answer:
$-\sin(r)$