• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Trigonometric Inverse

  • Thread starter vanmaiden
  • Start date
1. The problem statement, all variables and given/known data
I understand that y = sin -1 x. However, why is it that when one writes x = sin y, one leaves out the -1


2. Relevant 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]
 
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
1,663
Well, that is how inverse functions work.
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top