# 2_8notes - 1. ( 29-= x y 3 sin Range: ____________________...

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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( tells the phase shift (horizontal), 0 < gives a shift to the left & 0 gives a shift to the right Steps for Graphing B x A y + - = ) sin( or B x A y + - = ) cos( : 1. Determine the amplitude A and the period π 2 = T . 2. Determine the starting point of one cycle (period) of the graph, . 3. Determine the ending point of one cycle (period) of the graph, + 2 . 4. Divide the interval + 2 , into four subintervals, each of length 4 2 ÷ . 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. Graph the following functions. Show two cycles and label any key points.

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Unformatted text preview: 1. ( 29-= x y 3 sin Range: ____________________ 2. ( 29 + = 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 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( 2. B x A y +-= ) cos( 3. B x A y +-= ) cos(...
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## This note was uploaded on 03/15/2009 for the course MATH 114 taught by Professor Smith during the Spring '08 term at Michigan State University.

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2_8notes - 1. ( 29-= x y 3 sin Range: ____________________...

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