Determine the exact value of $\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$.

A) $\frac { \pi } { 2 }$

B) $\frac { \pi } { 4 }$

C) $\frac { \pi } { 3 }$

D) $\frac { \pi } { 6 }$

E) $\frac { 3 \pi } { 4 }$

Question

Determine the exact value of $\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$.

A) $\frac { \pi } { 2 }$

B) $\frac { \pi } { 4 }$

C) $\frac { \pi } { 3 }$

D) $\frac { \pi } { 6 }$

E) $\frac { 3 \pi } { 4 }$

Quizplus · Accepted Answer

The inverse cosine function returns an angle, which has a range of $[0,\pi]$. Since $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} =\frac{\sqrt{2}}{2}$, we can see that $\frac{\pi}{4}$ is an angle whose cosine is $\frac{\sqrt{2}}{2}$, hence $\cos^{-1}\left(\frac{\sqrt{2}}{2}\right) = \boxed{\frac{\pi}{4}}$ or B.

Determine the Exact Value Of cos⁡−1(22)\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)cos−1(22​​)

Determine the Exact Value Of $\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$