# January 26 th copyright2009merrydavidson 2 Example Determine the amplitude, period, and phase shift of y = 2sin (3x -  ) Solution: First factor out.

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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

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

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.

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

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

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.

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

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

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

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

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

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

Fill in summary page on WS.

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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