How can you explain that

sin(180-θ)=sinθ

using the unit circle??

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- Feb 5th 2014, 11:49 AMlaurettarosaUNIT CIRCLE question!
How can you explain that

sin(180-θ)=sinθ

using the unit circle?? - Feb 5th 2014, 12:06 PMromsekRe: UNIT CIRCLE question!
Attachment 30124

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

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

Now what does $\displaystyle 180-\theta$ 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 $\displaystyle \theta$ remains the same. - Feb 5th 2014, 01:20 PMlaurettarosaRe: UNIT CIRCLE question!
Thanks so much!!