CalcNotes0103-page10

CalcNotes0103-page10 - for sin u + v ( ) started with the...

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(Chapter 1: Review) 1.44 GROUP 1: SUM IDENTITIES Memorize: sin u + v () = sin u cos v + cos u sin v Think : “Sum of the mixed-up products” (Multiplication and addition are commutative, but start with the sin u cos v term in anticipation of the Difference Identities.) cos u + v () = cos u cos v ± sin u sin v Think : “Cosines [product] – Sines [product]” tan u + v () = tan u + tan v 1 ± tan u tan v Think : " Sum 1 ± Product " GROUP 2: DIFFERENCE IDENTITIES Memorize: Simply take the Sum Identities above and change every sign in sight! sin u ± v () = sin u cos v ± cos u sin v (Make sure that the right side of your identity
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Unformatted text preview: for sin u + v ( ) started with the sin u cos v term!) cos u v ( ) = cos u cos v + sin u sin v tan u v ( ) = tan u tan v 1 + tan u tan v Obtaining the Difference Identities from the Sum Identities: Replace v with ( v ) and use the fact that sin and tan are odd, while cos is even. For example, sin u v ( ) = sin u + v ( ) [ ] = sin u cos v ( ) + cos u sin v ( ) = sin u cos v cos u sin v...
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