find the exact value in degrees:  A.  y=arcsin(1/2) B.  y=arctan(-sqrt3)

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justaguide's profile pic

Posted on

You are only allowed to ask one question at a time.

I am responding to the first one.

y = arc sin (1/2)

=> y = 30 degrees

The required solution is 30 degrees.

giorgiana1976's profile pic

Posted on

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.

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