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y = arc sin (1/2)
=> y = 30 degrees
The required solution is 30 degrees.
We know that sin y = 1/2, so that arcsin (1/2) = y
y = 30 degrees
We also know that tan y = -sqrt 3 => arctan (-sqrt 3) = y
The tangent is negative in the 2nd and the 4th quadrants.
If the angley is in the 2nd quadrant, the angle y, for arctan (-sqrt 3) = y, is y = 180 - 60 = 120 degrees.
If the angle x is in the 4th quadrant, then x = 360 - 60 = 300 degrees.
The angle y for arcsin (1/2) = y is y = 30 degrees and the angle y for arctan (-sqrt 3) = y, are 120 degrees or 300 degrees.