Question

How do you find the exact value of `arcsin(sin((7pi)/3))`?

Answer 1

`arcsin(sin((7pi)/3)) = pi/3`

Explanation:

As an argument to a trigonometric function:
`color(white)("XXXX")` `(7pi)/3` is equivalent to `pi/3`
`color(white)("XXXX")` `color(white)("XXXX")`(since `(7pi)/3 = 2pi+pi/3`)

Provided `theta` is within `[0, pi]`
`color(white)("XXXX")` `arcsin(sin(theta)) = theta`
`color(white)("XXXX")` `color(white)("XXXX")`(basic definition)

So
`arcsin(sin((7pi)/3))`
`color(white)("XXXX")` `= arcsin(sin(pi/3))`
`color(white)("XXXX")` `= pi/3`