SOLUTION: 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
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{12}{5})
Normalize the tangent value to the unit circle. Since tangent is opposite over adjacent, the hypotenuse must be 
. Rewrite the tangent value:
\ =\ \frac{\ -\frac{12}{13}\ }{-\frac{5}{13}})
(minus signs because 
is in the third quadrant.)
\ =\ \pm\sqrt{\frac{1\ -\ \cos(\varphi)}{{2}}})
So:
\ =\ \pm\sqrt{\frac{1\ -\ \left(-\frac{5}{13}\right)}{{2}}}\ =\ \pm\sqrt{\frac{\frac{18}{13}}{2}}\ =\ \pm\frac{3\sqrt{13}}{13})
.
But since we know to be in the third quadrant, 
must be in the second quadrant where sine is positive, hence:
\ =\ \frac{3\sqrt{13}}{13})
John
My calculator said it, I believe it, that settles it
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