Video: Finding the Value of a Trigonometric Function Involving Special Angles

Evaluate sin 225°.


Video Transcript

Evaluate sine of 225 degrees.

To solve this, we can draw a picture. First, we want to identify the angle 225 degrees. Halfway around the circle is 180 degrees. And to get 225, we need to move forward 45 degrees. This angle measures 225 degrees. If we consider the unit circle, this point is located at negative one, negative one.

We know that the sine measure is the opposite over the hypotenuse. The sine of 225 degrees would be negative one over the measure of the hypotenuse. The hypotenuse is the 𝑐-value in the Pythagorean theorem, 𝑎 squared plus 𝑏 squared equals 𝑐 squared. But because we’re dealing with the 45-45-90-degree triangle, we recognize the hypotenuse as the square root of two. And the sine of 225 degrees is equal to negative one over the square root of two.

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