Question

assignment 8.3: inverse trigonometric functions
score: 14/27 answered: 8/14
question 9
evaluate the expression \\( \sin ^ { - 1 } \left( \cos \left( \frac { \pi } { 4 } \
ight) \
ight) \\).
give your answer as an exact value
question help: video 1 video 2 message instructor

Explanation:

Step1: Calculate the value of $\cos(\frac{\pi}{4})$

We know that $\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$.

Step2: Evaluate $\sin^{-1}(\frac{\sqrt{2}}{2})$

The range of the inverse - sine function $y = \sin^{-1}(x)$ is $[-\frac{\pi}{2},\frac{\pi}{2}]$.
We know that $\sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$.

Answer:

$\frac{\pi}{4}$