Trig Without Tears - Tutorials To Help You Develop Identities

[jaime2000]

http://oakroadsystems.com/twt/

I searched and it looked like no one had posted this before, so here it is. Trig without tears is an awesome site in which some guy explains trigonometry, from the basic functions of sine and cosine to the double and half angle identities. The interesting part is that the author, who believes it is wrong to use memorization as a substitute for thinking and disagrees with the memorization-based approach to identities regularly found in school, instead teaches you how to develop the identities in a way that is easy to follow and remember. I wish I had read this when I was taking pre-calculus last summer. It's great! ^.^

[Greek2Me64]

Here are links to tutorials for basic "right angle" trig that does NOT use the standard SOH CAH TOA mneumonic. The first tutorial shows you how to make a "Trig Tool", which elimininates memorizing a lot of formulas, the next two show you how to USE it.

http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html

http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html

http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html

[stevenb]

A good trig identity tip is that if you ever run into trouble doing (or remembering) a trig identity, you can always fall back on the following two Euler relations.

\cos x ={{e^{i x}+e^{-i x}}\over{2}}

\sin x ={{e^{i x}-e^{-i x}}\over{2 i}}

where i is the square root of negative one.

For example, take the famous one,

\sin ^2 x+\cos ^2 x =1

plug in the relations and one gets

{{(e^{i x}+e^{-i x})^2-(e^{i x}-e^{-i x})^2}\over{4}} =1

{{(e^{2i x}+2+e^{-2i x})-(e^{2i x}-2+e^{-2i x})}\over{4}} =1

{{4}\over{4}} =1

1 =1