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

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 𝑥-values are in terms of 𝜋: 𝜋 over two, 𝜋, three 𝜋 over two, two 𝜋. And then, 𝑦 are the real numbers.

So let’s think about the values on the unit circle. We begin at zero and then go counterclockwise. And we’re at 𝜋 over two and then we’re at 𝜋 and then three 𝜋 over two and then a full circle all the way around; that would be two 𝜋. So at zero, we have the value of zero; at 𝜋 over two, we’ve the value of one; at 𝜋, we’re at zero; at three 𝜋 over two, we’re at negative one; and then at two 𝜋, we’re at zero again just like at zero.

So these values we can recognize from the unit circle. We’re at one, zero and next we’re at zero, one. And then here, we’re at negative one, zero, and here we’re at zero, negative one. So these are all 𝑥𝑦 values. And the values that are on our graph are the 𝑦-values in pink.

So if we remember, the 𝑥-values represent the cosine function and the 𝑦-values represent the sine function. So that means our graph must be the sine function.