Question

Does...
1. sin(2pi + Ѳ) = -cos Ѳ
2. cos(2pi - Ѳ) = cos Ѳ

I don't know what to do with the pi's. My teacher never taught me how to check if equations are identities with pi in them. Please explain.

Answer 1

The unit circle

Let me ask...if you start



And you travel 2π around the circle...where will you end up?

Answer 2

it would be in the same place

Answer 3

Right...you would end up in the same exact place, meaning we can just ignore them and just worry about

1) \(\large sin(\theta) = -cos(\theta)\) and clearly that is NOT a correct statement

Does that make sense?

Answer 4

okay but what about if it wasn't 2pi? what would you do if it was something where you couldn't ignore it?

Answer 5

It would be the same for 2) as well

\(\large cos(2\pi - \theta) = cos(\theta)\) since 2π brings us back to the same place, we ignore it and just have

\[\large cos(-\theta) = cos(\theta)\] which *since we know cos is an odd function is correct

Answer 6

what do you mean an odd function?

Answer 7

cos is an even function
sin is an odd function

Answer 8

Oops, yup my mistake there!

Answer 9

okay how does that help?

Answer 10

It is an identity

\[\large cos(-\theta) = cos(\theta)\]

Answer 11

You said since cos in an odd function it is correct? what do you mean by that? How would it being an odd function help

Answer 12

i meant it being an even function

Answer 13

Yeah I did too, still sorry about that typo lol

So here maybe a visual would help with this...the graph of cos(x) is