Question

For what values of theta (in radians) is sin(theta)=-1

Answer 1

3pi/2

Answer 2

Basically, you look up the arc sine of -1 which is -1.5708 Radians or
which is -(PI/2) radians

Answer 3

Or you could consider the definition of the sine function: sin theta =opp/hyp,

and then write out sin theta = opp/hyp = -1/1,

and then draw (or picture in your mind) what angle has that sine. Hint: opp=-1; hyp=1.

Answer 4

I'm thinking that 1.5708 Radians = 90° and
-1.5708 Radians = -90°

so -90° = -1.5708 Radians = 270°

Answer 5

There are multiple solutions to this problem, because the sine function is periodic.

+3pi/2 and -pi/2 are certainly solutions.

But be careful: it is not correct to say that -90 deg = 270 deg. If you insist on writing an equation here,

write sin (-90 deg) = sin(270 deg).

since the sine is periodic, it's best to write the solutions in a way that shows that there are infinitely many solutions:

3pi/2 plus or minus 2pi*n, where n={0, plus or minus 1, plus or minus 2, etc.}.