# Homework Help: Sin and inverse sin multiplied

1. May 8, 2012

### binalbean

1. The problem statement, all variables and given/known data

Evaluate the following:

Sin^-1(sin(19*pi/7) in terms of pi

3. The attempt at a solution

i cant see any other way apart from the functions cancel to give 19pi/7 but checking on wolfram gives 2*pi/7, can anybody explain or help?

Thanks

2. May 8, 2012

### I like Serena

Welcome to PF, binalbean!

The inverse sine is defined to yield a result between -pi/2 and +pi/2.
So they do not just cancel.

The typical method is to draw a unit circle, find where the angle 19pi/7 is, and find the angle that has the same y coordinate but which is between -pi/2 and +pi/2.

3. May 8, 2012

### Staff: Mentor

The equation f-1(f(x)) = x is true only if x is in the domain of f, and f(x) is in the domain of f-1.

For example, ln(e-1) = -1, but eln(-1) is undefined. Here -1 is not in the domain of the natural log function.

4. May 8, 2012

### LCKurtz

And a nit-pick. The Sin-1 and sin aren't "multiplied". That is a composition of the two functions, or "function of a function".

5. May 9, 2012

### binalbean

Thanks very much for your help!! :D

6. May 9, 2012

### I like Serena

You're welcome. :)

This problem is an example that these conditions are not sufficient.
x also has to be in the image of f-1.

Btw, it's weird if f(x) is not in the domain of f-1.