CalcNotes0103-page15 - . There are no symbols in the last...

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(Chapter 1: Review) 1.49 GROUP 5: HALF-ANGLE IDENTITIES Instead of memorizing these outright, it may be easier to derive them from the Power-Reducing Identities (PRIs). We use the substitution ± = 2 u . (See Obtaining … below.) The Identities: sin 2 ² ³ ´ µ · 1 ¸ cos 2 cos 2 ² ³ ´ µ · 1 + cos 2 tan 2 ² ³ ´ µ · 1 ¸ cos 1 + cos = 1 ¸ cos sin = sin 1 + cos For a given , the choices among the ± signs depend on the Quadrant that 2 lies in. Here, the ± symbols indicate incomplete knowledge; unlike when we deal with the Quadratic Formula, we do not take both signs for any of the above formulas for a given
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Unformatted text preview: . There are no symbols in the last two tan 2 formulas; there is no problem there of incomplete knowledge regarding signs. One way to remember the last two tan 2 formulas: Keep either the numerator or the denominator of the radicand of the first formula, stick sin in the other part of the fraction, and remove the radical sign and the symbol....
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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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