Question

If sin theta = -0.89 determine two possible values for theta if 0 degrees < theta < 360.

Answer 1

\[\sin(\theta) = -0.89\]
\[\theta = \sin^-1(-0.89)\] That could be one possible way of figuring out an angle.

Answer 2

okay. any other?

Answer 3

Not sure since you have a negative 0.89.

Answer 4

You may be able to find another if it is not exactly the same by using:\[\sin^-1(\theta) = \frac{ 1 }{ \sin(\theta) } = \csc(\theta)\]

Answer 5

But you can not have a negative angle based on your 0 < theta < 360

Answer 6

Another way is adding or removing revolutions around the circle so

Answer 7

hope that makes sense
arcsin or inverse sin will give 2 angles both with equal reference angles
doing the arcsin of pos value yields the reference angle allowing you to find 2 angles in 3rd and 4th quadrants