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. .

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) (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.
***
given tanx=-5/8 (3π/2,2π)

Hypotenuse of reference right triangle in quadrant IV
=
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:=≈-0.2868..

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