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CalcNotes0103-page14

CalcNotes0103-page14 - cos 2 u To obtain the identity for...

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(Chapter 1: Review) 1.48 GROUP 4: POWER-REDUCING IDENTITIES (“PRIs”) (These are called the “Half-Angle Formulas” in some books.) Memorize: Then, sin 2 u = 1 ± cos 2 u ( ) 2 or 1 2 ± 1 2 cos 2 u ( ) tan 2 u = sin 2 u cos 2 u = 1 ± cos 2 u ( ) 1 + cos 2 u ( ) cos 2 u = 1 + cos 2 u ( ) 2 or 1 2 + 1 2 cos 2 u ( ) Actually, you just need to memorize one of the sin 2 u or cos 2 u identities and then switch the visible sign to get the other. Think: “sin” is “bad” or “negative”; this is a reminder that the minus sign belongs in the sin 2 u formula. Obtaining the Power-Reducing Identities from the Double-Angle Identities for
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Unformatted text preview: cos 2 u ( ) To obtain the identity for sin 2 u , start with Version 2 of the cos 2 u ( ) identity: cos 2 u ( ) = 1 ± 2 sin 2 u Now, solve for sin 2 u . 2 sin 2 u = 1 ± cos 2 u ( ) sin 2 u = 1 ± cos 2 u ( ) 2 To obtain the identity for cos 2 u , start with Version 3 of the cos 2 u ( ) identity: cos 2 u ( ) = 2 cos 2 u ± 1 Now, switch sides and solve for cos 2 u . 2 cos 2 u ± 1 = cos 2 u ( ) 2 cos 2 u = 1 + cos 2 u ( ) cos 2 u = 1 + cos 2 u ( ) 2...
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