CalcNotes0103-page12 - recall the Double-Angle Identities...

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(Chapter 1: Review) 1.46 Obtaining the Double-Angle Identities from the Sum Identities: Take the Sum Identities, replace v with u , and simplify. sin 2 u () = sin u + u () = sin u cos u + cos u sin u (From Sum Identity) = sin u cos u + sin u cos u (Like terms!!) = 2sin u cos u cos 2 u () = cos u + u () = cos u cos u ± sin u sin u (From Sum Identity) = cos 2 u ± sin 2 u tan 2 u () = tan u + u () = tan u + tan u 1 ± tan u tan u (From Sum Identity) = 2 tan u 1 ± tan
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Unformatted text preview: recall the Double-Angle Identities quickly! One possible exception: Since the tan 2 u ( ) identity is harder to remember, you may prefer to remember the Sum Identity for tan u + v ( ) and then derive the tan 2 u ( ) identity this way. If you’re quick with algebra, you may prefer to go in reverse: memorize the Double-Angle Identities, and then guess the Sum Identities....
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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