Because it's sin and it's negative I know it's not on the top two quadrants. How can I tell if it's either in quadrant three or quadrant 4? If it's in quadrant 3 then it's -90 degrees and if it's quadrant 4 it's -30 degrees but I don't know which of the two it's in
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Note that arcsin(-1/2) cannot possibly = -90°, since sin(-90°) = -1 (not -1/2)
But sin(-30°) and sin(-150°) = -1/2
-30 is in quadrant 3, -150 is in quadrant 4
arcsin(x) has range -90° ≤ arcsin(x) ≤ 90° (i.e. always in quadrant 4 or quadrant 1)
arcsin(-1/2) = -30°
But sin(-30°) and sin(-150°) = -1/2
-30 is in quadrant 3, -150 is in quadrant 4
arcsin(x) has range -90° ≤ arcsin(x) ≤ 90° (i.e. always in quadrant 4 or quadrant 1)
arcsin(-1/2) = -30°
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Yes: arcsin(x), asin(x), and sin⁻¹(x) are all the same as inverse sin(x)
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Since inverse sin has domain -pi/2 <= x <= pi/2, inverse sin(-1/2) is in the 4th quadrant. So, the angle is 30 degrees in the 4th quadrant which is 330 degrees.
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- 30 degs