How do you evaluate $arcsin^-1(-1/2)$ without a calculator?

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Answer 1 · 2018-05-25T17:37:54

$theta = 11/6 pi = 330^@$

Given: $arcsin^-1 (-1/2)$

I believe what you want is $arcsin (-1/2) = sin^-1(-1/2)$

$arcsin (-1/2)$ says, find me the angle that has a sine $= -1/2$ ,

or what is the angle $theta$ that yields $sin theta = -1/2$ ?

Since the $arcsin$ function has a limited domain: $-pi/2 <= theta <= pi/2$ , we will only need to look at the 4th quadrant due to the negative sign.

$theta = 11/6 pi = 330^@$

How do you evaluate arcsin^-1(-1/2)arcsin^-1(-1/2) without a calculator?