Trigonometric IdentitiesDate: 11/12/97 at 18:16:50 From: Steven Schoenherr Subject: Trigonometric Identities I have a huge test coming up on trig identities and was wondering what the best way to solve verification problems would be. Also, do I really have to memorize all of the Identities in order to understand them? Thanks, Steven Schoenherr Date: 11/12/97 at 21:00:46 From: Doctor Wilkinson Subject: Re: Trigonometric Identities There are some identities that you have to know, and others that you should be able to derive from the ones you have memorized. I divide the essential identities into three groups: (1) Identities that express all the trig functions in terms of the sine and cosine: tanx = sinx/cosx cotx = cosx/sinx secx = 1/cosx cscx = 1/sinx (2) sin^2(x) +cos^2(x) = 1 This is just the Pythagorean Theorem expressed in terms of trigonometry. Using (1) and (2) you can prove a whole bunch of other identities, and this saves you having to memorize them. For example, sec^2x - tan^2x = 1/cos^2x - sin^2/cos^2x (from group 1) = (1 - sin^2x)/cos^2x = cos^2x/cos^2x (from 2) = 1 (3) The addition formulas for sine and cosine: sin(x + y) = sin(x) cos(y) + cos(x) sin(y) and cos(x + y) = cos(x) cos(y) - sin(x) sin(y) From the formulas in (3) and the formulas in (1) you can derive addition formulas for the other functions such as the tan. You can also get the so-called double-angle formulas like sin(2x) = 2sin(x) cos(x) I also recommend doing a lot of practice problems, but keep the memorization down to just the identities I've mentioned already. -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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