SOLUTION: Solve this equation on the interval 0 θ < 2π. If there is no solution, enter NONE.
cos(2θ) = cos θ
(smallest value)- ___________ __
- __
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Question 970652: Solve this equation on the interval 0 θ < 2π. If there is no solution, enter NONE.
cos(2θ) = cos θ
(smallest value)- ______________
- ______________
(largest value) - ______________
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
cos 2x=2 cos^2x-1
2cos^2 x-1-cos x=0
2 cos^2 x- cos x -1=0 Factor.
(2cos x +1) (cos x-1)=0
cos x=1 cos x=(-1/2)
cos x=1 at 0 degrees Cos 0 deg=cos 2*0 degrees
cos x=(-1/2) at pi/3 or 120 degrees.
cos x= (-1/2) at 2pi/3 or 240 degrees.
smallest value is 0
largest value is 2 pi/3
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