Question

Having a graph of a trig function allows you to estimate values of the function or better yet take a function value and determine the angle required to make that. How many times will a sin function have a value of 1/2

Answer 1

$sin^{-1}\frac{1}{2}\\\frac{\pi}{6}+2\pi n$

A sine function will have a value of 1/2 infinity times. However, on the interval of a single period, a sine function will have a value of 1/2 one time.

Answer 2

That depends on what range of angles you explore.

Through the first circle's worth (360 degrees), the sine function
has the value of 1/2 twice ... at 30 degrees and at 150 degrees.