Question

Find all solutions of the equation. (Enter each answer in the form θ + 2πk, 0 ≤ θ < 2π. If there are any unused answer boxes, enter NONE in the last boxes.)

2cos^2(x)-cos(x)-1=0

Answer 1

You can factor this expression.

Answer 2

i factored it to get (2cos(x) + 1)(cos(x) - 1) = 0

Answer 3

\[(2\cos(x)+1)(\cos(x)-1)=0\]

Answer 4

now set each factor equal to zero and solve for x

Answer 5

Cos(x)= -1/2 and Cos(x)= 1

Answer 6

yes, but now you need to express all possible angles for which those ratios are correct

Answer 7

2pi/3, 4pi/3 and 2pi?

Answer 8

plus 2pik on all of them

Answer 9

yep

Answer 10

thank you!