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

What function is being represented on the graph?


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œ‹: ๐œ‹ over two, ๐œ‹, three ๐œ‹ over two, two ๐œ‹. 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œ‹ over two and then weโ€™re at ๐œ‹ and then three ๐œ‹ over two and then a full circle all the way around; that would be two ๐œ‹. So at zero, we have the value of zero; at ๐œ‹ over two, weโ€™ve the value of one; at ๐œ‹, weโ€™re at zero; at three ๐œ‹ over two, weโ€™re at negative one; and then at two ๐œ‹, 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.

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