Understanding Trigonometric Inverse Functions - Solving Homework Equations

[vanmaiden]

Homework Statement

I understand that y = sin ^-1 x. However, why is it that when one writes x = sin y, one leaves out the ^-1

Homework Equations

The Attempt at a Solution

I know that when you invert a trig function, the dependent variable essentially switches from y to x and the independent variable switches from x to y. However, why do you leave out the ^-1 when you write the inverse sin as x = sin y ?

 

[lanedance]

not sure if I understand the question, but if you start from
$$y = sin^{-1} x$$

take the sin of both sides
$$sin(y) = sin(sin^{-1} x) = x$$

 

[vanmaiden]

not sure if I understand the question, but if you start from
$$y = sin^{-1} x$$

take the sin of both sides
$$sin(y) = sin(sin^{-1} x) = x$$

I'm sorry I wasn't very clear. That answers my question though! I had no idea you could take the sin of the sin^-1(x) and it would cancel them out. Thank you!

 

[SteamKing]

Well, that is how inverse functions work.