# Math Help - UNIT CIRCLE question!

1. ## UNIT CIRCLE question!

How can you explain that
sin(180-θ)=sinθ
using the unit circle??

2. ## Re: UNIT CIRCLE question!

Originally Posted by laurettarosa
How can you explain that
sin(180-θ)=sinθ
using the unit circle??

Think about a line that goes from the center of the unit circle to it's perimeter and makes some angle $\theta$ with the x axis.

The sine of $\theta$ is the y coordinate of the intersection of that line and the unit circle because it's radius is 1.

Now what does $180-\theta$ do. It reflects this line about the y axis. The x coordinate of the intersection with the unit circle is multiplied by -1, and the y coordinate remains the same. Thus the sine of $\theta$ remains the same.

3. ## Re: UNIT CIRCLE question!

Thanks so much!!