Proof of Trigonometric Identities and Formulas

By:

Stephen Bismarck

While I was thinking of some ideas to put on these pages, I came across a college algebra and trigonometry book. I remember using all these formulas and had no idea where they came from and why were they right? The following proofs and illistrations can be easily incorperated into the curriculum of high school algebra or college algebra and trigonometry. I hope that people can find these useful and fun to figure out.

These proofs make one major assumption, that you know what the definition of the two basic trigonometry functions in a right triangle

If your wondering about Tan q it's just Sin q / Cos q :)

Let us start at the first one that comes to mind (Sin q)^2 +(Cos q )^2 = 1

GSP file

Proof

Cos(a+b) = Cos(a)Cos(b) - Sin(a)Sin(b)

Sin(a+b) = Sin(a)Cos(b) + Cos(a)Sin(b)

Double Angle Formulas

GSP file

Proof

Now what about those power reducing formulas

I'm not going to show the last one because it's the same as (Sin q)^2 / (Cos q)^2 remember

GSP file

Proof

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