Chapter 4.7, Problem 12E

a.

To determine

To find: The exact value of the expression $\arccos \left(-\sqrt{3}\right)$

Answer to Problem 12E

Not possible

Explanation of Solution

Given:

  $\arccos \left(-\sqrt{3}\right)$

Calculation:

The given expression is $\arccos \left(-\sqrt{3}\right)$

The domain of the inverse cosine function is $\left[-1,1\right]$

The value of $\sqrt{3}=1.732$

Here, $-1.732$ doesn’t lie in the interval $\left[-1,1\right]$

Therefore, there is no any angle whose cosine is $-2$

Thus, it is not possible to find the value of $\arccos \left(-\sqrt{3}\right)$

b.

To determine

To find: The exact value of the expression $\arcsin \left(\frac{\sqrt{2}}{2}\right)$

Answer to Problem 12E

  $\arcsin \left(\frac{\sqrt{2}}{2}\right)=\frac{\pi }{4}$

Explanation of Solution

Given:

  $\arcsin \left(\frac{\sqrt{2}}{2}\right)$

Calculation:

The given expression is $\arcsin \left(\frac{\sqrt{2}}{2}\right)$

The value of $\sin \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}$ and the angle $\frac{\pi }{4}$ lies in the interval $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$

Therefore, $\arcsin \left(\frac{\sqrt{2}}{2}\right)=\frac{\pi }{4}$