Express the given quantity in terms of sin x or cos x.
-$\sin \left( \frac { 7 \pi } { 2 } + x \right)$
A) $\sin x - \cos x$
B) $- \cos x - \sin x$
C) $\cos x$
D) $- \cos x$

Question

Quizplus · Accepted Answer

Using the formula for the sine of the sum of two angles, we have
$$\sin \left(\frac{7\pi}{2}+x\right) = \sin\frac{7\pi}{2}\cos x + \cos\frac{7\pi}{2}\sin x$$
Since $\sin\frac{7\pi}{2} = -1$ and $\cos\frac{7\pi}{2} = 0$, we have
$$\sin \left(\frac{7\pi}{2}+x\right) = (-1)\cdot \cos x + (0)\cdot \sin x = -\cos x$$ 
Therefore, the answer is D.

Express the Given Quantity in Terms of Sin X or Cos