# Question Video: Simplifying Trigonometric Expressions Using Related Angle Trigonometric Identities Mathematics

Simplify sin (360Β° β π).

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### Video Transcript

Simplify sin of 360 degrees minus π.

To do this, letβs consider the unit circle. Weβll let π be an angle in standard position. And the point π₯, π¦ will be the coordinates of the point of intersection between the unit circle and the terminal side of π. The sin of π will equal π¦ over one. Therefore, we can label this distance as sin of π. Now we want to know where 360 degrees minus π would fall on our unit circle. The angle 360 degrees minus π in a counterclockwise direction would look like this. To calculate the sin of 360 degrees minus π, we would use its reference angle.

Here, we have a reflection in the π₯-axis. Recall that weβve already said π¦ equals the sin of π. Therefore, negative π¦ equals the negative sin of π, which is also equal to the sin of 360 degrees minus π. This illustrates a principle that we know about the related angle identities for trigonometric functions. And that is that the sin of 360 degrees minus π is equal to the negative sin of π. Weβve been able to simplify sin of 360 degrees minus π and show that itβs equal to negative sin of π.