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# Using the Sine and Cosine Addition Formulas to Prove Identities - Problem 2

###### 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.

Let's prove this supplementary angle identities using the cosine and sine addition formulas. The supplementary angle identities are the ones that say sine of pi minus theta equals blank or cosine of pi minus theta equals blank.

Pi minus theta is the supplement of theta. Well the sine of a difference is sine, cosine, cosine, sine. Sine pi, cosine theta, cosine pi, sine theta and with sine the minus stays the same. The sine of pi 0, cosine of pi is -1, so it turns out that the sine of pi minus theta is equal to the sine of theta. That's a really important in resolving you use a lot when you're solving trigonometric equation involving sine.

Supplementary angles have the same output like 30 degrees and 150 degrees would have the same output, like 30 degrees and 150 degrees would have the same output, what about cosine is this true? Well for cosine of a difference we have cosine, cosine, sine, sine that's cosine pi, cosine theta minus sine pi, sine theta. Again cosine pi is -1, sine of pi is 0, so we're left with minus cosine theta it's not true. If you take the supplement of an angle, its cosine will be opposite.

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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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