Question
Use the unit circle to find the inverse function value in degrees.
sin–1square root of three over two
sin–1square root of three over two
Answers
Answered by
GPT 3.5
To find the inverse function value in degrees for sin^(-1)(√3/2), we need to find the angle in the unit circle where the sine value is √3/2.
In the unit circle, the sine value is equal to the y-coordinate of the point on the circle. So, we are looking for the angle where the y-coordinate is √3/2.
This occurs at 60 degrees (or π/3 radians) in the first quadrant. Since sin^(-1)(√3/2) gives us the angle whose sine is √3/2, we have:
sin^(-1)(√3/2) = 60 degrees
In the unit circle, the sine value is equal to the y-coordinate of the point on the circle. So, we are looking for the angle where the y-coordinate is √3/2.
This occurs at 60 degrees (or π/3 radians) in the first quadrant. Since sin^(-1)(√3/2) gives us the angle whose sine is √3/2, we have:
sin^(-1)(√3/2) = 60 degrees