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# Evaluating Sine and Cosine at Special Acute Angles - Problem 3

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

Pi over 3 is another special angle. I want to find the cosine and sine of Pi over 3. Now I’ve drawn the angle Pi over 3 on the unit circle point P is the point on the terminal side of Pi over 3 and I need to find the coordinates of Pi over3 in order to find the sine and cosine of the angle.

But I already know the coordinates of point Q which lies on the angle Pi over 6. The sine of Pi over 6 is ½ and the cosine of Pi over 6 is root 3 over 2 and that gives me the x and y coordinates. This is the x coordinate., this is the y coordinate of point Q.

Point Q is a refection of point P along the line y equals, y equals x. you can kind of see that because Pi over 3 is 60 degrees, Pi over 6 is 30 degrees. This angle is 30 degrees so there is symmetry across the diagonal. That means that to get the coordinates of point P all I need to do is interchange the coordinates of point Q. So point P has coordinates ½ root 3 over 2 and that means the cosine of Pi over 3 is ½ and the sine of 1/3 is root 3 over 2.

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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

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## Rommel · 10 months, 3 weeks ago

What if we memorize the unit circle? Is it still important to know this concept?