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## anonymous 5 years ago 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

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1. anonymous

You can factor this expression.

2. anonymous

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

3. anonymous

$(2\cos(x)+1)(\cos(x)-1)=0$

4. anonymous

now set each factor equal to zero and solve for x

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

plus 2pik on all of them

9. anonymous

yep

10. anonymous

thank you!

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