Evaluate $\arccos \frac { \sqrt { 3 } } { 2 }$ without using a calculator.
A) $- \frac { \pi } { 6 }$
B) $\frac { \pi } { 4 }$
C) $- \frac { 3 \pi } { 4 }$
D) $\frac { \pi } { 6 }$
E) $\frac { \pi } { 3 }$

Question

Quizplus · Accepted Answer

Recall that $\cos \frac{\pi}{6} = \frac{ \sqrt{3}}{2}$. Taking the inverse cosine of both sides gives $\frac{\pi}{6} = 	ext{arccos} \frac{\sqrt{3}}{2}$. However, since we want the answer to be negative (since cosine is negative in the second and third quadrants), the answer is $\boxed{	extbf{(D)}\ \frac{-\pi}{6}}$.

Evaluate arccos⁡32\arccos \frac { \sqrt { 3 } } { 2 }arccos23​​

Evaluate $\arccos \frac { \sqrt { 3 } } { 2 }$