Question

Please help. WILL MEDAL! cos3θ−1=0 @mathstudent55 @Kainui @sleepyjess @satellite73 @phi @zepdrix @robtobey

Answer 1

\[\cos 3\theta-1=0\]

Answer 2

\[\cos3\theta=1\]

Answer 3

This is where I get stuck.

Answer 4

sec brb :)

Answer 5

If it was \(\large\rm \cos x=1\), would you know how to proceed?

Answer 6

I think so.

Answer 7

It would be 0,

Answer 8

Good, cosine is the full length, 1 at an angle of 0.
So we would say x=0.

Answer 9

\[0 \le \theta < 360\]

Answer 10

I have to solve for all of these^ values.

Answer 11

So when \(\large\rm \cos(\color{orangered}{x})=1\),
we determined that \(\large\rm \color{orangered}{x}=0\)
Let's be a little more specific though,
we could add any number of full rotations to this angle 0, and still land at the same spot,\[\large\rm \color{orangered}{x}=0+2k \pi\]Ok with that weird step?

Answer 12

I don't understand.

Answer 13

cos(0) = 1
cos(0+2pi) = 1
cos(0+4pi) = 1
...
cos(0+2kpi) = 1

The k is some integer,
it's some amount of 2pi's.

Answer 14

Okay I got it.

Answer 15

you determined that 0 angle gives us this 1 length.