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y x- intercepts x

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y x x- intercepts

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Period = 2/|b| = 2/3 2 -2 /6 5/6 /2 Draw one full period of y=2sin(3x/2) 2/3 This is the graph of 2sin(3x). Now click to see the phase shift and to get 2sin(3x/2) /3 Amplitude = |a| = 2 Phase shift = -c/b = /6

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Graph one full period of sin(x /2) 1/2 a = 1, b = 1,c = /2 and d = 1/2 Amplitude = |a| = 1 Period = 2/b = 2 Phase shift = c/b = /2 Vertical translation: 1/2 units down y = sin(x) y = sin(x /2) y = sin(x /2) 1/2 1 1/2 1 3/2 Phase shift /2 units right Vertical translation units down Section 5.7 Question 43

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Graph one full period of 2sin(3x /2) +1 a = 2, b = 3,c = /2 and d = 1 Amplitude = |a| = 2 Period = 2/b = 2/3 Phase shift = c/b = /6 Vertical translation: 1 unit up 2 3 1 2 /6 /22/3 x y /3 This is the graph of 2sin(3x). Now click to see the phase shift, vertical translation and to get 2sin(3x/2)+1 1

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Graph one full period of sin(x+ /6) a = 1, b = 1,c = /6 Amplitude = |a| = 1 Period = 2/b = 2 Phase shift = c/b = /6 1 1 /2 3/222 x y /6 Section 5.7 Question 18 This is the graph of sin(x). Now click to see the phase shift and to get sin(x+/6)

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Graph one full period of cos(2x/3) a = 1, b = 2,c = /3 Amplitude = |a| = 1 Period = 2/b = Phase shift = c/b = /6 1 1 x y /2 /6/43/4 Section 5.7 Question 20 This is the graph of cos(2x). Now click to see the phase shift and to get cos(2x-/3) 7/6

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Graph one full period of y=(1/2)sin(x/3) a = 1/2, b = /3 Amplitude = |a| = 1/2 Period = 2/b = 6 1/2 1/2 3/2 9/2 6 x y 3

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2 22 1 1 In [0, ], In [, 2], 0 sinx 2sinx 2sinx sinx 0 Graph one full period of y=2sinx and y= sinx

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x y 2 2 2 Draw one full period of y = 2tan(x/2) a = 2 and b = 1/2, 4b = 2 Asymptotes: Lets draw asymptotes Mark 2 and 2 on the y-axis and /4b = /2 on the x- axis x = 2/4b = 2/2 = Now we can draw the graph Section 5.6 Question 29

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Graph one full period of (3/2)csc(3x) a = 3/2, b = 3 Period = 2/b = 2 /3 /6/3 /2 2/3 Section 5.6 Question 34 3/2 3/2

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Graph one full period of (1/3)tanx a = 1/3, b = 14b = 4 Period = /|b| = /4 /4 1/3 1/3 Section 5.6 Question 22 /2/2

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Graph one full period of 2cscx x y a =2, b = 1 Period = 2/b = 2 2 22 /2 3/2 22 Section 5.6 Question 28

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Graph one full period of -3sec(2x/3) x y a = 3, b = 2/3 Period = 2/b = 3 3 3 3/43/29/433 Section 5.6 Question 36

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x y 3 3 3 Draw one full period of y = 3tan(3x) a = 3 and b = 3, 4b = 12 Asymptotes: Lets draw asymptotes Mark 3 and 3 on the y-axis and /4b = /12 on the x-axis x = 2/4b = 2/12 = /6 Period = /b = /2 Now we can draw the graph

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x y 1/2 1/2 Draw one full period of y = (1/2)cot(2x) a = 1/2 and b = 2, 4b = 8 Asymptotes: Lets draw asymptotes Mark 1/2 and 1/2 on the y-axis and /8, 2/8, 3/8 and 4/8 on the x-axis x = /b = /2 and x = 0(y-axis) Period = /b = /2 Now we can draw the graph

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Graph one full period of y=3/2sin(x /4+3 /4) a =3/2, b = 1/4,c = 3/4 Amplitude = |a| = 3/2 Period = 2/b = 8 Phase shift = c/b = 3 2 66 88 3/2 3/2 3 x y 44 This is the graph of y=3/2sin(x/4). Now click to see the phase shift and to get y=3/2sin(x/4+3/4)

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Graph one full period of y= sec(x /2 )+1 x y a = 1, b = 1, c = /2, d = 1 Period = 2/|b| = 2 Phase shift = c/b = /2 Vertical translation : (d =) 1 unit up 1 1 3/222 /2 2 cos(x) sec(x) Click to shift /2 unit to right Click to shift 1 unit up | |||

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Graph one full period of y= csc(x/3-/12)+4 x y a = 1, b = 1/3, c = /3, d = 4 Period = 2/|b| = 6 Phase shift = -c/b = /4 Vertical translation: 4 unit up 1 11 3/2 33 9/2 66 || | | /4 5 3 sin(x/3) csc(x/3)

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1/2sin(3x) 0 1/2sin(3x) 0 Sketch the graph of y = |(1/2)sin(3x)| /3 2/3 -/3 -2/3 -1/2 1/2 0 Section 5.5 Question 48

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Sketch the graph of y = cos 2 (x) 1 /2 -/2 -- /4 3/2 -3/2 -/4 Section 5.5 Question 65 1/2

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Sketch the graph of y = sin|x| 22 -- -2 1 0 Section 5.5 Question 68 y = sin|x| = sin(x) if x 0 sin(x) if x 0