SOLUTION: If the value of sin&#1138; is 1/2, determine the measure of &#1138; if &#960;/2 < &#1138; < 3&#960;/2. Answer must be exact values.

Algebra ->  Trigonometry-basics -> SOLUTION: If the value of sin&#1138; is 1/2, determine the measure of &#1138; if &#960;/2 < &#1138; < 3&#960;/2. Answer must be exact values.       Log On


   



Question 926580: If the value of sinѲ is 1/2, determine the measure of Ѳ if π/2 < Ѳ < 3π/2. Answer must be exact values.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since +pi%2F2+%3C+theta+%3C+%28+3%2Api+%29%2F2+,
+theta+ is either in the 2nd quadrant
or the 3rd quadrant.
Since the sin is negative in the 3rd
quadrant, the angle must be in the 2nd
-----------------------------------
The +arcsin%28+1%2F2+%29+=+pi%2F6+
The angle in the 2nd quadrant that makes
this angle with the horizontal axis is:
+theta+=+pi+-+pi%2F6+
+theta+=+%28+5%2Api%29%2F6+