# Inverse function

1. Nov 18, 2016

### Karol

1. The problem statement, all variables and given/known data
Simplify:
$$\sin^{-1}(2\sin^{-1}0.8)$$

2. Relevant equations
Inverse sine: $y=\sin^{-1}(x)~\rightarrow~\sin(y)=x$
$$\sin^2(x)+\cos^2(x)=1$$

3. The attempt at a solution
The inner parenthesis: $\sin y=0.8$ . In the drawing it's alpha's sine.
Now i double the α and the question wants the high edge in the drawing. how to find it?

2. Nov 18, 2016

### SammyS

Staff Emeritus
That problem seems very strange to me.

It would be much more expected to be asked to simplify something like:

$\sin\left(2 \sin^{-1} (0.8)\right)$

3. Nov 18, 2016

### Math_QED

Are you sure that's the correct question? It seems undefined to me.

4. Nov 18, 2016

### haruspex

Looking at the diagram, that is how Karol interpreted it.
@Karol, what formulae do you know for sin(2α) or sin(α+β)?

5. Nov 19, 2016

### Karol

$$\sin(2\alpha)=2\sin(\alpha)\cos(\alpha)$$
$$\sin^2(\alpha)+\cos^2(\alpha)=1~\rightarrow~\cos(\alpha)=0.6$$
$$\sin(2\alpha)=2\cdot 0.8 \cdot 0.6$$

6. Nov 19, 2016

### SammyS

Staff Emeritus
That looks fine, if you're trying to find $\ \sin\left(2 \sin^{-1} (0.8)\right) \, .$

7. Nov 19, 2016

### Math_QED

Also, if you want to type an implication '$\Rightarrow$', write 'Rightarrow' in Latex instead of 'rightarrow'.

8. Nov 20, 2016

### Karol

Thanks everybody, you are great!