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# Using the Sine and Cosine Addition Formulas to Prove Identities - Problem 1

###### 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.

I want to prove some more identities using the sine and cosine addition formulas. Let's prove what I call the add pi identities. This will give us an identity for the sine of theta plus pi, so I know theta plus pi equals blank and I want to do one for cosine as well.

Now first for the sine of theta plus pi, I need the sine of a sum identity and the sine of a sum goes sine, cosine, cosine, sine; so sine theta, cosine pi, cosine theta, sine pi. And with sine the plus stays the same remember sine same and that gives me sine of theta times cosine of pi is -1 just refer to the unit circle if you forget that and cosine of theta sine of pi is 0 and so that just gives me minus sine theta, so that's kind of interesting if you add pi to the input, you get the opposite output.

Let's see if that is true for cosine. The cosine sum identity goes cosine, cosine, sine, sine; cosine theta, cosine pi, sine theta, sine pi and with cosine remember c for change, the plus changes to minus. So it's cosine theta times -1 minus sine theta times 0. Yeah again we get minus cosine theta, so add pi and you get the opposite output, it's true for cosine too.

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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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