Question

How do you find the exact value of `sin^-1[sin(-pi/10)]`?

Answer 1

`sin^-1[sin(-pi/10)]=-pi/10`

Explanation:

`sin^-1[sin(-pi/10)]`

A simple way to understand this is from the fact that: `color(green)(sin^-1)` (also denoted byt `color(green)arcsin`) is the inverse trig function of `color(green)sin`

So if you `sin` an angle, you get an real number that lies between `-1` and `1`

On the other hand if you `sin^-1` the answer got previously, you get back the angle.

In the present case, let's say you originally had the angle `-pi/10`

Now, you when you `color(red)sin` it you obtain `sin(-pi/10)`

Then, if you `color(red)(sin^-1)` it this time you will get back the angle: `-pi/10`

That is `sin^-1` of `sin(-pi/10)` is `-pi/10`