Question

Write cos(3theta)=-1 in a+bk form.

Answer 1

\[\cos(3\theta)=-1\implies 3\theta=\pi +2k \pi \implies \theta=\frac{\pi}{3}+\frac{2k \pi}{3}\]\[k \in Z\]

Answer 2

Excuse me for asking, but how did you get 30 degrees, if 180/3 is 60?

Answer 3

If you don't know that the cos function is valued -1 at the odd multiples of pi, you need to study your unit circle some more.

Answer 4

My answer is given in radian measure.

Answer 5

I didn't get thirty; pi/3 is 60 degrees.

Answer 6

I see. I believe I was supposed to do that. My math teacher closed my assignment at 11... It restricted me from typing it in.

Answer 7

So, you divided 3 from pi, then added that to 2kpi/3, which is 360/3 or 180, which is in fact where cos -1, correct?

Answer 8

\[\cos \left( 3\theta \right)=-1\]\[\cos \left( 3\theta \right)=\cos \pi\]\[3\theta=\pi+k2\pi\]\[\theta=\frac{\pi}{3}+k\frac{2\pi}{3}\]or\[3\theta=-\pi+k2\pi\]\[\theta=-\frac{\pi}{3}+k\frac{2\pi}{3}\]

Answer 9

I think you get the second solution by the negative integer values of k in the first solution.

Answer 10

I'm pretty sure 360/3 isn't 180..... more like 120. Regardless, you have to learn to think in radians.

Answer 11

Whoops!! Looked at it wrong. Lol.