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Trigonometric Inverse

  • Thread starter vanmaiden
  • Start date
102
1
1. 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


2. Homework Equations



3. 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

Homework Helper
3,304
2
not sure if I understand the question, but if you start from
[tex] y = sin^{-1} x [/tex]

take the sin of both sides
[tex] sin(y) = sin(sin^{-1} x) = x [/tex]
 
102
1
not sure if I understand the question, but if you start from
[tex] y = sin^{-1} x [/tex]

take the sin of both sides
[tex] sin(y) = sin(sin^{-1} x) = x [/tex]
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! :smile:
 

SteamKing

Staff Emeritus
Science Advisor
Homework Helper
12,794
1,665
Well, that is how inverse functions work.
 

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