# 2_8notes - Math 114 Section 2.8 Phase Shift Section 001...

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Math 114 Section 2.8 Phase Shift Section 001 Translations of the sine and cosine graphs. B x A y + - = ) sin( ϕ ϖ B x A y + - = ) cos( ϕ ϖ ϖ ϕ tells the phase shift (horizontal), 0 < ϕ gives a shift to the left & 0 ϕ gives a shift to the right Steps for Graphing B x A y + - = ) sin( ϕ ϖ or B x A y + - = ) cos( ϕ ϖ : 1. Determine the amplitude A and the period ϖ π 2 = T . 2. Determine the starting point of one cycle (period) of the graph, ϖ ϕ . 3. Determine the ending point of one cycle (period) of the graph, ϖ ϕ ϖ π + 2 . 4. Divide the interval + ϖ ϕ ϖ π ϖ ϕ 2 , into four subintervals, each of length 4 2 ÷ ϖ π . 5. Use the endpoints of the subintervals to find the five key points on the graph. --- apply the amplitude change, reflection, and vertical shift 6. Fill in one cycle of the graph. 7. Extend the graph to include the number of cycles requested.

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Unformatted text preview: 1. ( 29-= x y 3 sin Range: ____________________ 2. ( 29 π + = x y 2 cos 3 Range: ____________________ 3. --= 2 2 cos 2 x y Range: ____________________ 4. ( 29 1 4 2 sin 2 +--= x y Range: ____________________ 6. Write an equation of the sine function that has the given characteristics: Amplitude: 4 Period: 4 3 π Phase Shift: 4-7. Write an equation of the cosine function that has the given characteristics: Amplitude: -2 Period: 3 Phase Shift: 4 1 Determining the Equation when Given the Graph 1. B x A y +-= ) sin( ϕ ϖ 2. B x A y +-= ) cos( 3. B x A y +-= ) cos( ϕ ϖ...
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