Question

Solve 2cos²x-1-cosx=0
Interval= 0≤x<2π
Please show steps

Answer 1

let\[t=\cos x\]u have\[2t^2-t-1=0\]now factor it or solve by quadratic equation formula

Answer 2

im supposed to end up with radians for my answer

Answer 3

@Shi

Answer 4

What mukushla said is a good step to get your answer, which will be in radians. Can you factor that equation?

Answer 5

Yea I just factored it. Now im stuck finding the solutions within the interval.

Answer 6

ok what did you factor it into? you dont have to worry about the interval just yet

Answer 7

x=1/2
x=1

Answer 8

you basically got it, I think the correct answers up to that point are t = -1/2 and t = 1
I used t just so we dont get confused

ok after that you convert t back into cos(x)

Answer 9

so you have
cos(x) = -1/2
and cos(x) = 1

following so far?

Answer 10

ok

Answer 11

we look at cos(x) = 1 first
at what value of x does cos(x) = 1?

Answer 12

0

Answer 13

yup, thats one of your answers.

same thing for the second equation, cos(x) = -1/2
I recommend looking at a unit circle since there are 2 values, and taking the inverse of both sides only gives you one answer

Answer 14

Ok thanks, i figured it out. Its not as bad as it seems lol

Answer 15

haha yeah, figuring out what to do is always the hard part. gl with the rest of your hw

Answer 16

Thanks