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

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2 January 26 th copyright2009merrydavidson

3 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

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

5 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.

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

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

8 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.

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

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

11 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 H: y=1/3 L:y=-1/3 x-axis y-axis M:y=0

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

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

14 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

15 Fill in summary page on WS.

16 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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