SOLUTION: if tan0=8/3 in quadrant 3, what are cos20, sin0/2, cos0/2

Algebra ->  Trigonometry-basics -> SOLUTION: if tan0=8/3 in quadrant 3, what are cos20, sin0/2, cos0/2      Log On


   

Question 304682: if tan0=8/3 in quadrant 3, what are cos20, sin0/2, cos0/2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if tan0=8/3 in quadrant 3, what are cos20, sin0/2, cos0/2
-------------
Angle is th (theta)
Hypotenuse = sqrt(73)
sin(th) = -8/sqrt(73) = -8sqrt(73)/73
cos(th) = -3/sqrt(73) = -3sqrt(73)/73
-----------------------
cos(2th) = cos^2(th) - sin^2(th)
= 9/73 - 64/73 = -55/73
-----------------------------
cos(th/2) = sqrt((1+cos(th))/2)
= +-sqrt%28%2873+-+3sqrt%2873%29%29%2F146%29
--------------------------------
sin(th/2) = sqrt((1-cos(th))/2)
= +-sqrt%28%2873%2B3sqrt%2873%29%29%2F146%29