Question

You may use the unit circle shown below to help you answer this question.

Which of these are true statements about the sine function? Choose all that are correct.

A
For any value of θθ , sin(−θ)=sin(θ)sin(−θ)=sin(θ) .
B
For any value of θθ , sin(−θ)=−sin(θ)sin(−θ)=−sin(θ) .
C
The sine function is an odd function.
D
The sine function is an even function.
E
The sine function has a period of ππ .
F
The sine function has a period of 2π2π .

Answer 1

B, C, F

Explanation:

For the first part, this is the negative angle identity of the sine and cosine function. These identities are:

`\cos(-\theta)=\cos(\theta)`

`\sin(-\theta)=-\sin(\theta)`

Then (I believe I am reading this right), B is true. I am unsure because of the repeated value in the middle. The next piece is that sine is odd. By definition, an odd function is one such that:

`f(-x)=-f(x)`

As we just demonstrated with the identities, sine obeys this and therefore is odd. Cosine, on the other hand, is even because it follows:

`f(-x)=f(x)`

Last, the period of sine, or the distance on the x-axis it takes to complete one full wavelength, and the answer is
`2\pi`. If you look at a graph of the sine function, you will find that the wave repeats itself at the
`2\pi` mark and it does this with cosine as well.