Question

Can someone tell me where I went wrong in this problem?

2 cos (x/3) - Squareroot of 2=0

Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)

Answer 1

Screenshot with my answer that I submitted

Answer 2

So when you found the solutions for x/3, what were they?
pi/4 and what else?

Answer 3

cos(x/3)=sqrt 2/2

Answer 4

pi/4 and 7pi/4

Answer 5

So \[\frac{ \pi }{ 4 } and \frac{ 7\pi }{ 4 }\]

Answer 6

Mmmm ok that looks right!

Answer 7

\[\cos \frac{ x }{ 3 } =\frac{ \sqrt{2} }{ 2 }\]

Answer 8

So what would be the final answer?

Answer 9

I think you just mixed up your multiplication by 3 maybe?

3*7pi/4 = 21pi/4

Answer 10

And why are you adding 5n(pi) in the first solution set?
I'm really confused .. need to see your steps.

Answer 11

In this screenshot they have included an example of this problem and the answer, if it helps!

Answer 12

I am not sure what I was doing! I was going by examples from the internet trying to figure it out

Answer 13

\[\large\rm \cos\left(\frac x3\right)=\frac{\sqrt2}{2}\]So within one rotation this gives us two solutions.\[\large\rm \frac x3=\frac{\pi}{4}\]\[\large\rm \frac x3=\frac{7\pi}{4}\]But we want the entire solution sets, so we need to allow for rotation,\[\large\rm \frac x3=\frac{\pi}{4}+2n \pi\]\[\large\rm \frac x3=\frac{7\pi}{4}+2n \pi\]From this point, solve for x by multiplying through by 3.

Answer 14

\[\frac{ 3\pi }{ 4 } + 6n \pi ?\]

Answer 15

Ya that's one of the solution sets.
Do the same for the other one.

Answer 16

21π/4+6nπ ?

Answer 17

Yes

Answer 18

So those two are the final solutions?

Answer 19

Yes

Answer 20

Thank you so much!!!