When finding two angles for theta: sin (theta) = -4/5:
find the two possible angles for theta "given theata is between -pi and pi"
Ignoring the "given " part, solving for the two angles seems relatively simple : invsin (-4/5) gives refereance angle of 53.13 and quadrant must be 3 and 4 due sin is negative, so angles are 233.13 and 306.87. But what do they mean by theta must be bewteen -pi and pi? answers must be between -180 and zero?

Question

When finding two angles for theta: sin (theta) = -4/5:
find the two possible angles for theta "given theata is between -pi and pi"
Ignoring the "given " part, solving for the two angles seems relatively simple : invsin (-4/5) gives refereance angle of 53.13 and quadrant must be 3 and 4 due sin is negative, so angles are 233.13 and 306.87.  But what do they mean by theta must be bewteen -pi and pi?  answers must be between -180 and zero?

michele_laino · Answer

we have the subsequent drawing:
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