CalcNotes0103-page15

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 ² ³ ´ µ ¶ · formulas; there is no problem there of incomplete knowledge regarding signs. One way to remember the last two tan 2 ² ³ ´ µ ¶ · 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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