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I can write trig functions from a graph
Warm Up Write the equation of the ππππ function with amplitude 4, shift right πππΒ°, with a period of 9 and a midline at π=π Write the equation of the graph (ππ,π) (π,βπ) (πππ,βπ)
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Warm Up Write the equation of the ππππ function with amplitude 4, shift right πππΒ°, with a period of 9 and a midline at π=π
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Warm Up Write the equation of the graph (π,βπ) (ππ,π) (πππ,βπ)
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Buffalo Problem
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Buffalo Problem
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A Correctionβ¦ π¦= asin π π₯ββ +π This meansβ¦ before identifying a horizontal shift, you must first factor out π.
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A Correctionβ¦ π¦= asin π π₯ββ +π Example: π¦=2 sin 3π₯βπ π¦=2sinβ‘ 3 π₯β π 3 Shift: right π 3
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Examples π¦= sin 3π₯+180Β° π¦= cos 2π₯βπ π¦=5cosβ‘ 4π₯+ π 2 π¦=βsinβ‘ 3π₯β90Β°
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Examples π¦= sin 3π₯+180Β° π¦= cos 2π₯βπ π=π¬π’π§β‘[π π+ππΒ° ] π=πππ π πβ π
π
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Examples π¦=5cosβ‘ 4π₯+ π 2 π¦=βsinβ‘ 3π₯β90Β° π=ππππ π π+ π
π π=βπππ π πβππΒ°
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Break
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What could we use to find x?
Trig Identity x What could we use to find x? 3 7 Pythagorean Theorem π 2 + π 2 = π 2
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What could we use to find x?
Trig Identity What could we use to find x? x πππ(ππΒ°) πππ(ππΒ°) π ππ 2 (60Β°)+ πππ 2 (60Β°)= π₯ 2
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Trig Identity π ππ 2 (60Β°)+ πππ 2 (60Β°)= π₯ 2 3 2 2 + 1 2 2 = π₯ 2
= π₯ 2 = π₯ 2 1= π₯ 2 π₯=1
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What could we use to find x?
Trig Identity What could we use to find x? x πππ(πππΒ°) πππ(πππΒ°) π ππ 2 (135Β°)+ πππ 2 (135Β°)= π₯ 2
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Trig Identity π ππ 2 (135Β°)+ πππ 2 (135Β°)= π₯ 2 2 2 2 + β 2 2 2 = π₯ 2
β = π₯ 2 = π₯ 2 1= π₯ 2 π₯=1
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Pythagorean Identity πππ 2 π₯+ π ππ 2 π₯=1
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Give your answer in positive degrees.
AA5a Problem 4 Give your answer in positive degrees.
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