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**We need to sketch the graph of y = 3sin(5t+90)**

Trig Transformations y y=sint t jhvjvjvh We need to sketch the graph of y = 3sin(5t+90)

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Trig Transformations y period = 360 y=sint t Crosses x axis at 0, 180, 360, 540

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Trig Transformations y y=sin(t+90) t Horizontal translation of -90 Crosses x axis at 90, 270, 450 Inside = horizontal opposite

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Trig Transformations y Wave frequency = 5 y=sin(5t+90) Period = = 72 72 t Horizontal stretch of Inside = horizontal opposite Crosses x axis at 18, 54, 90

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Trig Transformations y y=3sin(5t+90) t Vertical stretch of factor 3 Outside = vertical same

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Trig Transformations y y=3sin(5t+90)+2 t +2 Vertical translation of +2 Outside = vertical same

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Sketch the graph of y = 1sin(t + 45) y = 2sin(t + 30) y = 3sin(2t – 90) y = 4sin(3t + 60)

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**y = 1sin(t + 45) y = 2sin(t + 30) 1 2 y = 3sin(2t – 90)**

Translate horizontally by –30 Stretch vertically factor of 2 Translate horizontally by –45 y = 3sin(2t – 90) y = 4sin(3t + 60) 3 4 Translate horizontally by +90 Stretch horizontally by ½ Stretch vertically factor of 3 Translate by horizontally –60 Stretch horizontally by 1/3 Stretch vertically factor of 3

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**Finding the equation from a graph**

Y= Asin(t+ ) + c The mean line is at y = 4 The graph has been translated vertically by +4

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**Finding the equation from a graph**

Y= Asin(t+ ) + 4 The graph has been translated vertically by +4 So c = 4

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**Finding the equation from a graph**

Y= Asin(t+ ) + 4 2 The graph has an amplitude of 2 So the graph has been stretched vertically by a factor of 2

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**Finding the equation from a graph**

Y= 2sin(t+ ) + 4 2 The graph has an amplitude of 2 So A = 2

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**Finding the equation from a graph**

Y= 2sin(t+ ) + 4 180 The period = 180 =

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**Finding the equation from a graph**

Y= 2sin(2t + ) + 4 180 =

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**Finding the equation from a graph**

Y= 2sin(2t + a) + 4 Phase shift a = x time for mean line = 2 Phase shift a = 2 x 45 = 90

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**Finding the equation from a graph**

Y= 2sin(2t – 90) + 4 As the sin graph has been translated to the RIGHT then a = –90

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2Sin(x+45) Sin(x+30) 2Sin(x+60)+1 Sin(x-15)+2

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Sin(x–30)–1 2Sin(x–30) 3Sin(x+45)–1 3Sin(x+90)+ 0.5

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**Finding the equation from a graph**

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6.5 & 6.7 Notes Determining the transformations to trigonometric functions.

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