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

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Unformatted text preview: Math 114 A. Basic Identities Reciprocal Identities: Section 3.3 Trig Identities Section 001 1 csc θ 1 csc θ = sin θ sin θ = Quotient Identities: 1 sec θ 1 sec θ = cosθ cosθ = 1 cot θ 1 cot θ = tan θ tan θ = tan θ = sin θ cosθ cot θ = cosθ sin θ Pythagorean Identities: sin 2 θ + cos2 θ = 1 Cofunction Identities: 1 + tan 2 θ = sec 2 θ 1 + cot 2 θ = csc 2 θ π sin − θ = cos θ 2 π csc − θ = sec θ 2 π cos − θ = sin θ 2 π sec − θ = csc θ 2 π tan − θ = cot θ 2 π cot − θ = tan θ 2 Even-Odd Properties: sin ( − θ ) = − sin θ csc( − θ ) = − csc θ cos( − θ ) = cos θ sec( − θ ) = sec θ tan ( − θ ) = − tan θ cot ( − θ ) = − cot θ 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” Use identities fraction Multiply by the conjugate Factor Split up a fraction Simplify a complex You CANNOT add/subtract from one side to the other or multiply/divide on both sides! 1. sec θ • cot θ = csc θ 2. 1 + cot 2 ( − θ ) = csc 2 θ 3. sin θ ( cot θ + tan θ ) = sec θ 4. ( csc θ − 1) ( csc θ + 1) = cot 2 θ 5. csc 4 θ − csc 2 θ = cot 4 θ + cot 2 θ 6. 1 − sin 2 θ = − cos θ 1 − cos θ 7. sin θ cos θ tan θ = 2 2 cos θ − sin θ 1 − tan 2 θ 8. tan θ − cot θ + 2 cos 2θ = 1 tan θ + cot θ 9. cos θ + sin θ − sin 3 θ = cot θ + cos 2 θ sin θ π csc − x + csc x 2 = sin x + cos x 10. π cot x + cot − x 2 11. cos(− x ) = sec x + tan x 1 + sin( − x) ...
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3_3notes - Math 114 A Basic Identities Reciprocal...

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