mac1147_lecture27_1_c

mac1147_lecture27_1_c - 324 L27 Trigonometric Identities;...

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Unformatted text preview: 324 L27 Trigonometric Identities; Sum and Difference Formulas; Double-angle and Half-angle Formulas Basic Trigonometric Identities Quotient Identities : sin tan cos θ θ θ = cos cot sin θ θ θ = Reciprocal Identities : 1 csc sin θ θ = 1 sec cos θ θ = 1 cot tan θ θ = Pythagorean Identities : 2 2 sin cos 1 θ θ + = 2 2 tan 1 sec θ θ + = 2 2 cot 1 csc θ θ + = 325 Example : Use algebraic technique and the basic trigonometric identities to simplify. ( ) 2 2 cot 1 tan θ θ + = 2 2 cos sin sin cos θ θ θ θ − = 2 2 1 t a n 1 c o t θ θ + = + ( ) tan sec θ θ − = 326 Example : Perform the operations and simplify. cos sin sin 1 cos θ θ θ θ + = + ( ) 2 1 t a n 2 t a n α α + − = 2 1 cot tan tan α α α + = 2 csc 1 t − = 327 Example : Factor: 3 3 sin cos θ θ − = 2 2sin 3sin 1 α α + + = 328 Example : Verify the trigonometric identities. 1 sec tan sec tan α α α α = + − 2 sin sec cos cos β β β β = − 329 4 4 2 sin cos 2sin 1 θ θ θ − = − cos sec tan 1 s i n β β β β = + − 330...
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This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture27_1_c - 324 L27 Trigonometric Identities;...

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