3_3notes - Math 114 A Basic Identities Reciprocal...

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Math 114 Section 3.3 Trig Identities Section 001 A. Basic Identities Reciprocal Identities: sin csc θ θ = 1 cos sec θ θ = 1 tan cot θ θ = 1 csc sin θ θ = 1 sec cos θ θ = 1 cot tan θ θ = 1 Quotient Identities: tan sin cos θ θ θ = cot cos sin θ θ θ = Pythagorean Identities: sin cos 2 2 1 θ θ + = 1 2 2 + = tan sec θ θ 1 2 2 + = cot csc θ θ Cofunction Identities: θ θ π cos 2 sin = - θ θ π sin 2 cos = - θ θ π cot 2 tan = - θ θ π sec 2 csc = - θ θ π csc 2 sec = - θ θ π tan 2 cot = - Even-Odd Properties : ( 29 θ θ sin sin - = - ( 29 θ θ cos cos = - ( 29 θ θ tan tan - = - ( 29 θ θ csc csc - = - ( 29 θ θ sec sec = - ( 29 θ θ cot cot - = - B. Establishing Identities 1. Try starting with the side that is more complicated. 2. Rewrite sums or differences of quotients as a single quotient. 3. Sometimes rewriting one side in terms of sine and cosine only will help. 4. Always keep your goal in mind! Other Tricks: Multiply by “1”
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