SOLUTION: Find all positive vales of theta less than 360degrees that satisfy the equation costheta=2+3cos2theta. Express your answers to the nearest ten minutes or nearest tenth of a degree.

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Question 830491: Find all positive vales of theta less than 360degrees that satisfy the equation costheta=2+3cos2theta. Express your answers to the nearest ten minutes or nearest tenth of a degree.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all positive vales of theta less than 360degrees that satisfy the equation costheta=2+3cos2theta. Express your answers to the nearest ten minutes or nearest tenth of a degree.
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(0 cos%28theta%29=2%2B3cos%282theta%29
cos%28theta%29=2%2B3%282cos%5E2%28theta%29-1%29
cos%28theta%29=2%2B6cos%5E2%28theta%29-3%29
6cos%5E2%28theta%29-cos%28theta%29-1=0%29
%283cos%28theta%29%2B1%29%282cos%28theta%29-1%29=0%29
..
%283cos%28theta%29%2B1%29=0
cos%28theta%29=-1%2F3
theta=109.5˚, 250.5˚(in quadrants II and III in which cos<0)
or
%282cos%28theta%29-1%29=0%29
cos%28theta%29=1%2F2
theta=60˚,300˚(in quadrants I and IV in which cos>0)