SOLUTION: Find sin( α - β) if cos(α)=1/2 and sin(β)= \frac{ \sqrt{3} }{2} , given that α and β DO NOT lie in quadrant I.

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Question 1071272: Find sin( α - β) if cos(α)=1/2 and sin(β)= \frac{ \sqrt{3} }{2} , given that α and β DO NOT lie in quadrant I.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
For cos a=1/2 not in Q1 requires a=300 degrees
For sin b= sqrt(3)/2 not in Q1 requires b=120 degrees
Also, when cos is +, sin is - if they are not in the first quadrant.
When sin is +, cos is - when they are not in the first quadrant
When one of these is 1/2, the value of the other is -sqrt(3)/2, if they are not in the first quadrant.
sin (a-b)=sin a*cos b-cos a*sin b
=-(sqrt(3)/2)*-(1/2)-(1/2)(sqrt(3)/2)
=sqrt(3)/4-sqrt(3)/4=0
sin (180)=0