CalcNotes0103-page16

CalcNotes0103-page16 - (Chapter 1: Review) 1.50 Obtaining...

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Unformatted text preview: (Chapter 1: Review) 1.50 Obtaining the Half-Angle Identities from the Power-Reducing Identities (PRIs): For the sin 2 identity, we begin with the PRI: sin 2 u = () 1 cos 2u 2 Let u = sin 2 sin 2 2 = 2 , or = 2u . 1 cos 2 ( by the Square Root Method ) 1 cos 2 =± Again, the choice among the ± signs depends on the Quadrant that The story is similar for the cos 2 and the tan What about the last two formulas for tan 2 2 2 identities. ? The key trick is multiplication by trig conjugates. For example: tan 2 =± =± 1 cos 1 + cos (1 cos ) (1 (1 + cos ) (1 (1 cos ) cos cos ) ) 2 =± =± =± =± 1 cos 2 (1 cos ) 2 sin 2 1 cos sin 1 cos sin lies in. 2 ( because blah2 = blah ) ...
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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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