Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

Simplify sin (360Β° β π).

Simplify sin of 360 degrees minus π.

To do this, letβs consider the unit circle. Weβll 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 weβve 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. Weβve been able to simplify sin of 360 degrees minus π and show that itβs equal to negative sin of π.

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy