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Evaluating Sine and Cosine at Other Special Angles - Problem 3 4,140 views

Teacher/Instructor 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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