# UNIT CIRCLE question!

• February 5th 2014, 12:49 PM
laurettarosa
UNIT CIRCLE question!
How can you explain that
sin(180-θ)=sinθ
using the unit circle??
• February 5th 2014, 01:06 PM
romsek
Re: UNIT CIRCLE question!
Quote:

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

Attachment 30124

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.
• February 5th 2014, 02:20 PM
laurettarosa
Re: UNIT CIRCLE question!
Thanks so much!!