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Warm Up Verify that the equation is an identity.

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Section/Topic5.4b Sum/Difference Identities for Sine and Tangent. CC High School Functions Trigonometric Functions: Prove and Apply trigonometric identities ObjectiveStudents will be able to verify identities using all the previously learned ID and the Sum/Diff ID for Sine and Tangent. HomeworkPage 214-216 (3-8 all, 9-65 odd) due Tue, 12/10 Quiz 5.3 to 5.4 next Tuesday 12/10/13 Trig Game Plan Date: 12/09/13

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Sum and Difference Identities for Tangent Fundamental identity We can use the cosine sum and difference identities to derive similar identities for sine and tangent. Sum identities Multiply numerator and denominator by 1.

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Sum and Difference Identities for Tangent Multiply. Simplify. Fundamental identity

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Sum and Difference Identities for Tangent Replace B with –B and use the fact that tan(–B) to obtain the identity for the tangent of the difference of two angles.

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Tangent of a Sum or Difference tan ( A ± B ) = tan A ± tan B 1 tan A tan B ± - -

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Example WRITING FUNCTIONS AS EXPRESSIONS INVOLVING FUNCTIONS OF θ Write each function as an expression involving functions of θ. (a)(a) (b)

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Find the exact value of Example 1(d) FINDING EXACT SINE AND TANGENT FUNCTION VALUES

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5.4 Example 1 Finding Exact Sine and Tangent Function Values (cont.) (b) Example 1(e) FINDING EXACT SINE AND TANGENT FUNCTION VALUES

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5.4 Example 1 Finding Exact Sine and Tangent Function Values (cont.) (c) Example 1(g) FINDING EXACT SINE AND TANGENT FUNCTION VALUES

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Verify that the equation is an identity. Combine the fractions. Example 4a VERIFYING AN IDENTITY USING SUM AND DIFFERENCE IDENTITIES

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5.4 Example 4 Verifying an Identity Using Sum and Difference Identities (cont.) Expand the terms. Combine terms. Factor. So, the identity is verified. Example 4a VERIFYING AN IDENTITY USING SUM AND DIFFERENCE IDENTITIES

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Remember an identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established.

Remember an identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established.

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