Find all the solutions between 0 and 2pi (2 cos^3 t + cos^2 t − 2 cos t − 1 = 0)

This factors into (cos(t) - 1)(cos(t) + 1)(2cos(t) + 1) = 0 so  (i) cos(t) = 1   (ii) cos(t) = -1  (iii) cos(t) = -1/2

 

(i) cos(t) = 1  implies t = 0 or 2pi

 

(ii) cos(t) = -1 implies t = pi

 

(iii) cos(t) = -1/2 implies t = pi/3 or t = 5pi/3

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