SOLUTION: If tan &#945; = 12/5, &#960; < &#945; < 3 &#960;/2, and sin &#946; = 2/3, 0< &#946; < &#960;/2, find 1. sin &#945;/2 2. cos (&#945;+ &#946;) 3. sin (&#945;+ &#946;)/2

Algebra ->  Trigonometry-basics -> SOLUTION: If tan &#945; = 12/5, &#960; < &#945; < 3 &#960;/2, and sin &#946; = 2/3, 0< &#946; < &#960;/2, find 1. sin &#945;/2 2. cos (&#945;+ &#946;) 3. sin (&#945;+ &#946;)/2      Log On


   

Question 635549: If tan α = 12/5, π < α < 3 π/2, and sin β = 2/3, 0< β < π/2, find
1. sin α/2
2. cos (α+ β)
3. sin (α+ β)/2
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Normalize the tangent value to the unit circle. Since tangent is opposite over adjacent, the hypotenuse must be . Rewrite the tangent value:



(minus signs because is in the third quadrant.)



So:

.

But since we know to be in the third quadrant, must be in the second quadrant where sine is positive, hence:





John

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