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# Evaluating Sine and Cosine at Other Special 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.

For finding the sine and cosine of a special angles, this problem asks find the cosine and sine when theta equals minus 5 Pi over 3. So I’ve graphed -5 Pi over 3 and remember negative angles are clockwise angles.

This is minus 5 times Pi over 3 Pi over 3 is 60 degrees and this is minus 300 degrees and that means that the reference angle is going to be 60 degrees or Pi over 3. The first thing you do is find the cosine and sine of Pi over 3.

Cosine of Pi over 3 is one half and the sine of Pi over 3 is root 3 over 2. The cosine and sine of -5 Pi over 3 are going to be related to these two. The cosine of -5 over 3 would be plus or minus the cosine of Pi over 3, and the sine of -5 Pi over 3 we plus or minus the sine of Pi over 3.

Now -5 Pi over 3 terminates in the first quadrant and that means this point has both coordinates positive. And that means the cosine and sine are both is going to be positive so both of these guys will end up positive and the cosine and sine are one half and root 3 over 2 respectively.

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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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