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L23_filled - Ex(P2 Express in terms of the first power of...

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1 Day 27 Lecture 23 for 4/14/2011 Last (day) of the Identities L22 –Sum and Difference Recap! Memorize and or learn how to derive. The arrows indicate the order you can derive them. Slide: 2of 13 is 0
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2 L22 –Old Problems, New Details. Ex: Verify the identity… Ex: Solve on the interval . Slide: 3of 13 is 0 L23 –Multi-Angle Identities and others These derive from the Sum and Difference of Angle identities! Observe! u can be anything… They even help with graphing . Ex: Graph . Slide: 4of 13 is 0
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3 L23 –Typical Trig. Problem Ex: If and is in quadrant II, find 1) 2) Slide: 5of 13 is 0 L23 –More Down And Out Identities Ex: Write as an algebraic expression. Ex: Write in terms of . Slide: 6of 13 is 0
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4 L23 –Power-Reducing Formulas The power reducing formulas are all derived from the double angle identities for ____________. Ex: Express in terms of the first power of cosine. Slide: 7of 13 is 0 L23 –Half-Angle Formulas The half angle formulas are derived from the power reducing formulas on the last slide by making the substitution _________.
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Unformatted text preview: Ex (P2): Express in terms of the first power of cosine. Slide: 8 of 13 is 0 The choice of + or – depends on the quadrant in which u/2 lies. 5 L23 – Half-Angle Formulas Cont’d. Ex (P3): Find the exact value of . Ex (P7): Find if and x is in quadrant II. Slide: 9 of 13 is 0 L23 – The Possibilities are Endless The sum of difference of angle identities can be used to derive formulas for ___________________ a Product of Trig. Functions into a Sum of Trig. Functions and vice versa. Slide: 10 of 13 is 0 6 L23 – Application of Prod. To Sum / Sum to Prod. Ex: Find the exact value: P2 ) P3) P7) Slide: 11 of 13 is 0 L23 – For Verification Purposes. Ex: Verify Ex: Solve the equation in the interval . P2 ) Slide: 12 of 13 is 0 L23 – f The Last Examples 7 L23 – f The Last Examples P3 ) Slide: 13 of 13 is 0 L23 – f The Last Examples P7 ) Slide: 14 of 13 is 0...
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