Find the exact value of the expression whenever it is defined. (If an answer is undefined, enter UNDEFINED.)

Question

a.) sin^-1 (√2⁄2)

Answer 1

sin^-1(√2 / 2) = 45^o ( = π/4 radians)

To see this, draw a right triangle with one leg along the x-axis, one leg parallel to the y-axis, and finally draw the hypotenuse from the origin to the end of the leg parallel to y-axis. Label the hypotenuse 2, and the leg parallel to the y-axis √2. Now the length of the leg along the x-axis is √ (2² - (√2)² ) = √ (4 - 2) = √2 which means the triangle drawn has angles 45-90-45.

Answer 2

this is asking what angle has a sin of (sq root 2)/2 . that would be 45degrees or pi/4 radians and 135 degrees or 3pi/4 radians. These repeat every cycle (2pi radians) so final answer in radians is

(pi/4) + (2pi)n where n is an integer

and (3pi/4) +(2pi)n