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.