SOLUTION: if tan theta=1/2, and theta is between pi, and 3pi/2 (3rd quadrant i think) find the exact value of cos(theta/2)

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Question 921906: if tan theta=1/2, and theta is between pi, and 3pi/2 (3rd quadrant i think) find the exact value of cos(theta/2)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
if tan theta=1/2, and theta is between pi, and 3pi/2 (3rd quadrant i think) find the exact value of cos(theta/2)
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use x for theta
tanx=1/2
hypotenuse of reference right triangle in quadrant III=sqrt%281%5E2%2B2%5E2%29=sqrt%281%2B4%29=sqrt%285%29
cosx=-2%2Fsqrt%285%29

Check: w/calculator
tanx=1/2 (Q3)
x=206.565
x/2=103.28
cos(x/2)=cos(103.28)≈-0.2297
exact value=-sqrt%28%28sqrt%285%29-2%29%2F%282sqrt%285%29%29%29≈-0.2297