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January 26 th copyright2009merrydavidson

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2 Example Determine the amplitude, period, and phase shift of y = 2sin (3x - ) Solution: First factor out the 3 y = 2 sin 3(x - /3) Amplitude = |A| = 2 period = 2 /B = 2 /3 phase shift = C/B = /3 right

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Section 4.5 1) Fill in the sine value for each given angle on the worksheet.

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4.5 2) Put these values on the coordinate plane using the angle measures on the x axis and the sine value on the y axis. 0 will be at the origin.

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3) Sketch in the curve. (not straight lines)

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4) The curve oscillates between ____ and ____. What is the range of the sine curve? ______ 1 [-1, 1]

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How to graph the sine curve. Start at the origin – or the MIDDLE go MIDDLE go HIGH go LOW go MIDDLE THE LEFT SIDE of the graph IS THE OPPOSITE.

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5) Graph y = 2 sin The amplitude is 2 The period 360 0 because B is 1. How many sections on each side? Label them. -360 0 -270 0 -180 0 -90 0 0 0 90 0 180 o 270 0 360 o Put dots on the lines for middle, high, middle, low. H:y=2 L:y=-2 M:y=0 y-axis x-axis

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6) Graph y = sin2 The amplitude is 1 The period 180 0 because B is 2. How many sections on each side? Label them. -180 0 -135 0 -90 0 -45 0 0 0 45 0 90 o 135 0 180 o Put dots on the lines for middle, high, middle, low. y-axis x-axis H:y=1 M:y=0 L:y=-1

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7)graph What do you know? A is 1/3, reflect over x-axis (go middle then LOW), B is pi/2, x means radians. What is the period? = 4 4 notches to the right and left. -4 -3 -2 -1 0 1 2 3 4 H: y=1/3 L:y=-1/3 x-axis y-axis M:y=0

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8) Graph y = sin +2 The amplitude is 1; But the graph is shifted up 2. The period 360 0 because B is 1. y-axis x-axis H:y=3 M:y=2 L:y=1 -360 0 -270 0 -180 0 -90 0 0 0 90 0 180 o 270 0 360 o

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9)graph What do you know?A is 1, B is 1, theta means 90 degrees right. What is the period? 360 0 4 notches to the right and left. H:y=1 L:y=-1 90 0 start at +90 0. -270 0 -180 0 -90 0 0 0 180 0 270 o 360 0 450 o Draw in y-axis LAST. y = sin ( - 90 0 ) x-axis y-axis M:y=0

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Write the equation for the given graph using the origin as the start point. What is the period? What is the amplitude? Find “B”. y = 2cos2x Is this sine or cosine? cosine

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Fill in summary page on WS.

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Quiz next class over: * Graph sine and cosine curves with transformations. *Answer questions about amplitude, period, phase shift and vertical shift. *Write the equation for a sine and/or cosine graph from given information. *Given a graph, find specific attributes.

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Period and Amplitude Changes

Period and Amplitude Changes

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