SOLUTION: Find all exact solutions on [0, 2𝜋). (Enter your answers as a comma-separated list.) 2 cos^2(t) + cos(t) = 1

Question 1205306: Find all exact solutions on [0, 2𝜋). (Enter your answers as a comma-separated list.)
2 cos^2(t) + cos(t) = 1
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

given:

Find all exact solutions on [, )

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all exact solutions on [, )

Answer by ikleyn(52834) (Show Source): You can put this solution on YOUR website!
.
Find all exact solutions on [0, 2𝜋). (Enter your answers as a comma-separated list.)
2 cos^2(t) + cos(t) = 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write the original equation in the standard quadratic form = 0. Factor left side (2cos(t)-1) * (cos(t)+1) = 0. Case 1. 2cos(t) - 1 = 0 ---> cos(t) = ---> t = or t = . Case 2. cos(t) + 1 = 0 ---> cos(t) = -1 ---> t = . ANSWER. The set of solutions is , and , in ascending order.

Solved.

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