CalcNotes0103-page1 - x = sin x cos x and cot x = cos x sin...

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(Chapter 1: Review) 1.35 TOPIC 3: TRIGONOMETRY II PART A: FUNDAMENTAL TRIG IDENTITIES (IDs) Memorize these in both “directions” (i.e., left-to-right and right-to-left). Reciprocal Identities csc x = 1 sin x sec x = 1 cos x cot x = 1 tan x sin x = 1 csc x cos x = 1 sec x tan x = 1 cot x Warning : Remember that the reciprocal of sin x is csc x , not sec x . Note : We typically treat “0” and “undefined” as reciprocals when we are dealing with trig functions. Your algebra teacher will not want to hear this, though! Quotient Identities tan
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Unformatted text preview: x = sin x cos x and cot x = cos x sin x Pythagorean Identities sin 2 x + cos 2 x = 1 1 + cot 2 x = csc 2 x tan 2 x + 1 = sec 2 x Tip : The 2 nd and 3 rd IDs can be obtained by dividing both sides of the 1 st ID by sin 2 x and cos 2 x , respectively. Tip : The squares of csc x and sec x , which have the “Up-U, Down-U” graphs, are all alone on the right sides of the last two IDs. They can never be 0 in value. (Why is that? Look at the left sides.)...
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