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Evaluating Sine and Cosine at Other Special Angles - Problem 1

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.

We're finding the sine and cosine of other special angles, right now I want to find the cosine and sine of -135. I’ve drawn the angle -135 degrees on the unit circle in standard position and remember that finding the cosine and sine it means find the coordinates of point p.

The first step is to identify the reference angle and the reference angle is the angle between the terminal side of your given angle on the x axis and that would be 45 degrees, then calculate the sine and cosine of 45 degrees.

Hopefully you have these memorized you really should memorize them if you haven’t because these come up so often. Cosine of 45 degrees is root 2 over 2 and sine of 45 degrees is root 2 over 2. The next step is that the actual values of the cosine and sine of -135 are going to be these with a plus or minus of both of then you just need to figure out what the sine is based in the quadrant.

So cosine of -135 is little space root 2 over 2. Add a plus or minus and the sine of -135 little space root 2 over 2. Now point p is in the third quadrant and both coordinates are going to be negative here so both of these are going to be negative well that’s it.

Always remember when you are finding the sine or cosine of an angle that is in a cube, find the reference angle identify the cosine and sine if that angle and then use your knowledge of quadrants and sines to figure out why do you put your plus or minus in front of the answer.

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