Question

final exam (precalculus)
score: 22/25 answered: 22/25
question 23
evaluate the following expressions. your answer must be an exact angle in radians and in the interval 0, π. example: enter pi/6 for π/6.
(a) cos^(-1)(0)=
(b) cos^(-1)(1)=
(c) cos^(-1)(√2/2)=

Explanation:

Step1: Recall cosine - inverse values

We know that if $\cos\theta = x$, then $\cos^{-1}(x)=\theta$ for $\theta\in[0,\pi]$.

Step2: Solve (a)

Since $\cos(\frac{\pi}{2}) = 0$ and $\frac{\pi}{2}\in[0,\pi]$, $\cos^{-1}(0)=\frac{\pi}{2}$.

Step3: Solve (b)

Since $\cos(0)=1$ and $0\in[0,\pi]$, $\cos^{-1}(1) = 0$.

Step4: Solve (c)

Since $\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ and $\frac{\pi}{4}\in[0,\pi]$, $\cos^{-1}(\frac{\sqrt{2}}{2})=\frac{\pi}{4}$.

Answer:

(a) $\frac{\pi}{2}$
(b) $0$
(c) $\frac{\pi}{4}$