Question

Please help!
4cos (theta) + 1= 2cos (theta)

Answer 1

@jim_thompson5910

Answer 2

@robtobey

Answer 3

\(4\cos(\theta) + 1 = 2\cos(\theta)\) right?

Answer 4

yes!

Answer 5

For the moment, let \(x = \cos(\theta)\)

Answer 6

Now you have \(4x + 1 = 2x\)

Answer 7

Solve for x

Answer 8

2x=-1?

Answer 9

To finish solving for x, divide both sides by 2 right?

Answer 10

ohh, yes!

Answer 11

you would get x= -1/2

Answer 12

Also, I'm going to have to ask you to change your username to something with a more positive connotation.

Answer 13

lol, will do

Answer 14

Which means

\(\cos(\theta) = -\dfrac{1}{2}\)

Answer 15

Now take inverse cosine of both sides to isolate \(\theta\)

Answer 16

so the inverse cosine would be 120 degrees?

Answer 17

and 240 degrees

Answer 18

which would be 2pi/3 and 4pi/3?

Answer 19

2pi/3 is correct

Answer 20

From where did you get 4pi/3 ?

Answer 21

from 240 degrees

Answer 22

i was suppose to find 0< theta< 2pi. that means the whole unit circle right? I forgot to write that in the original question D:

Answer 23

http://www.wolframalpha.com/input/?i=inverse+cosine+%28-1%2F2%29%2C+0+%3C+theta+%3C+2pi

Answer 24

thank you so much