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Evaluating Sine and Cosine at Other Special Angles - Problem 2 4,121 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.

In finding the sine and cosine of other special angles this problem asks me to find the cosine and sine of 11 Pi over 6. So I’ve drawn the angle 11 Pi over 6 it's just 3 degrees short of a full revolution. When you define the coordinates x and y of point p with the terminal side crosses the unit circle.

The method for this is first to identify the reference angle which is Pi over 6 and then calculate the sine and cosine of Pi over 6. Sine of Pi over 6 equals a 1/2 cosine of Pi over 6 is root 3 over 2. Then the sine and cosine of 11 Pi over 6 is going to be plus or minus these values, cosine of 11 Pi over 6 plus or minus root 3 over 2 I’ll feel it in later.

Sine 11 Pi over 6 plus or minus 1/2. Now look at what quadrant the terminal side lies in, it's in quarter to four and here the y values are negative. So the sine is going to be negative but the cosine will be positive and definition is a problem for us.

Cosine of 11 Pi over 6 is root 3 over 2 sine of 11 Pi over 6 is -1/2.

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