Question

how to find the exact value of sin-1(-sqrt(2)/2)

Answer 1

use a unit circle

Answer 2

ok I know that 7pi/4 is -sqrt(2)/2 but what does it mean by sin-1

Answer 3

that usually indicates that it is looking for the inverse of the function

Answer 4

Yes, it is the inverse sin function.

Answer 5

You can write it like
\[\sin ^{-1}\left( \frac{ -\sqrt{2} }{ 2 } \right)=x\]

Answer 6

Which is the same thing as\[\sin(x) = \frac{ -\sqrt{2} }{ 2 }\]

Answer 7

The inverse sin cancels out the sin to help you solve for x.

Answer 8

Make sense, @alyrivera ?