Find the exact value of the composition.
-$$\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$$
A) $\frac { 2 \pi } { 3 }$
B) $\frac { 4 \pi } { 5 }$
C) $\frac { \pi } { 6 }$
D) $\frac { \pi } { 3 }$

Question

Quizplus · Accepted Answer

$\sin \frac { 7 \pi } { 6 }$ is $-\frac{1}{2}$. The range of $\cos^{-1}$ is $[0, \pi]$. Thus, $\cos^{-1}(-\frac{1}{2})$ is the angle in this range whose cosine is $-\frac{1}{2}$, which is $\frac { 2 \pi } { 3 }$.

Find the Exact Value of the Composition cos⁡−1(sin⁡7π6)\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)cos−1(sin67π​)

Find the Exact Value of the Composition $\cos ^ { - 1 } \left( \sin \frac { 7 \pi } { 6 } \right)$