find the exact value of the real number y if it exists. do not use a calculator.\nselect the correct answer…

find the exact value of the real number y if it exists. do not use a calculator.\nselect the correct answer below and, if necessary, fill in the answer box to complete your choice.\na. y = cos ^ { - 1 } ( \frac { sqrt { 2 } } { 2 } ) = \frac { pi } { 2 } \n(simplify your answer. type an exact answer, using pi as needed. use integers or fractions for any numbers in the expression.)\nb. cos ^ { - 1 } ( \frac { sqrt { 2 } } { 2 } ) does not exist.

find the exact value of the real number y if it exists. do not use a calculator.\nselect the correct answer below and, if necessary, fill in the answer box to complete your choice.\na. y = cos ^ { - 1 } ( \frac { sqrt { 2 } } { 2 } ) = \frac { pi } { 2 } \n(simplify your answer. type an exact answer, using pi as needed. use integers or fractions for any numbers in the expression.)\nb. cos ^ { - 1 } ( \frac { sqrt { 2 } } { 2 } ) does not exist.

Answer

Explanation:

Step1: Recall the range of the inverse cosine function

The range of (y = \cos^{-1}(x)) is ([0,\pi]).

Step2: Find the angle whose cosine is (\frac{\sqrt{2}}{2})

We know that (\cos\left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}) and (\frac{\pi}{4}\in[0,\pi])

Answer:

A. (y=\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)=\frac{\pi}{4})