Question 1183085
putting them on the same axis is tricky, but it can be done.


we'll work in radians.


the graph of y = sin(x) is shown below.


<img src = "http://theo.x10hosting.com/2021/071805.jpg" >


the graph of y = sin^-1(x) is shown below:


<img src = "http://theo.x10hosting.com/2021/071806.jpg" >


the difficulty is that:


when you graph y = sin(x), x is the angle and y is the trig function value.


when you graph y = sin^-1(x), x is the trig function value and y is the angle.


to graph them on the same axes, let the x-axis remain as the angle.


the functions are y = sin(x) and y = sin^-1(sin(x)).


that graph looks like this:


<img src = "http://theo.x10hosting.com/2021/071807.jpg" >


the blue graph is y = sin(x).
the red graph is y = sin^-1(x).


when x = pi/2, y = sin(x) = 1 and y = sin^-1(sin(x)) = pi/2, as shown on the graph.


the coordinate point for y = sin^-1) is shown as (pi/2,pi/2)
that means the x-value is pi/2 and the y-value is pi/2).
the x-value is pi/2, which is the angle.


y = sin(x) is equal to 1.
the coordinate points are (pi/2,1)
this is what is shown on the blue graph.


y = sin^-1(sin(x)) is equal to sin^-1(1) which is equal to pi/2.
the coordinate points are (pi/2,pi/2)
this is what is shown on the red graph.


keep in mind that the function y = sin^-1(sin(x)) will always make the value of y equal to the value of x.


not matter what value of x you choose, y will always be equal to x.


for example, if x = pi/4, sin(pi/4) = .7071067812.


sin^-1(.7071067812) = .7853981634.
divide that by pi and it becomes .25 * pi which is the same as pi/4.


sin-1(sin(pi/4) is equal to pi/4.


sin^-1(sin(pi/2) is equal to pi/2 as shown on the graph.