SOLUTION: Find the exact value of tangent of theta over 2 given tangent of theta = negative 5 over 8 and theta is between 3 pi over 2 and 2 pi. .

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Question 945488: Find the exact value of tangent of theta over 2 given tangent of theta = negative 5 over 8 and theta is between 3 pi over 2 and 2 pi. .
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of tangent of theta over 2 given tangent of theta = negative 5 over 8 and theta is between 3 pi over 2 and 2 pi.
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given tanx=-5/8 (3π/2,2π)
tan%28x%2F2%29=sinx%2F%281%2Bcosx%29
Hypotenuse of reference right triangle in quadrant IV
=sqrt%285%5E2%2B8%5E2%29=sqrt%2825%2B64%29=sqrt%2889%29
sinx=-5/√89=-5√89/89
cosx=8/√89=8√89/89

..
Check:
tanx=-5/8 (Q4)
x≈327.9946˚
x/2≈162.997˚
tan(x/2)=tan(162.997≈-0.2868..(from calculator)
exact value as computed:=%28-5sqrt%2889%29%29%2F%2889%2B8sqrt%2889%29%29≈-0.2868..