# Question Video: Figuring Out the Rule of a Trigonometric Function Drawn in a Given Graph Mathematics

What function is being represented on the graph?

01:21

### Video Transcript

What function is being represented on the graph?

On our graph, we can see that the ๐ฅ-values are in terms of ๐: ๐ over two, ๐, three ๐ over two, two ๐. And then, ๐ฆ are the real numbers.

So letโs think about the values on the unit circle. We begin at zero and then go counterclockwise. And weโre at ๐ over two and then weโre at ๐ and then three ๐ over two and then a full circle all the way around; that would be two ๐. So at zero, we have the value of zero; at ๐ over two, weโve the value of one; at ๐, weโre at zero; at three ๐ over two, weโre at negative one; and then at two ๐, weโre at zero again just like at zero.

So these values we can recognize from the unit circle. Weโre at one, zero and next weโre at zero, one. And then here, weโre at negative one, zero, and here weโre at zero, negative one. So these are all ๐ฅ๐ฆ values. And the values that are on our graph are the ๐ฆ-values in pink.

So if we remember, the ๐ฅ-values represent the cosine function and the ๐ฆ-values represent the sine function. So that means our graph must be the sine function.