Question

Given that `sin(theta) = -4/5`, how do you find the two possible angles for θ, given that `-pi < theta ≤ pi`?

Answer 1

`sin x = -4/5 = -0.8`

Calculator gives --> x = -53.15 deg

On the trig unit circle, there are 2 arcs that have the same sin value (-0.8), within the interval`(-pi, pi).`

`x = 180 + 53.13 = 233.13,` and

`x = 360 - 53.13 = 306.87` deg