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Published byJaheim Godsil Modified about 1 year ago

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

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

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

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

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

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

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

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12 34 y = 1sin(t + 45) y = 2sin(t + 30) y = 3sin(2t – 90) y = 4sin(3t + 60) Translate horizontally by +90 Stretch horizontally by ½ Stretch vertically factor of 3 Translate horizontally by –45 Translate horizontally by –30 Stretch vertically factor of 2 Translate by horizontally –60 Stretch horizontally by 1 / 3 Stretch vertically factor of 3

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

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Finding the equation from a graph The graph has been translated vertically by +4 So c = 4 Y= Asin( t+ ) + 4

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

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Finding the equation from a graph The graph has an amplitude of 2 So A = 2 Y= 2 sin( t+ ) + 4 2

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Finding the equation from a graph The period = 180 = Y= 2sin( t+ )

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Finding the equation from a graph Y= 2sin( 2 t + ) + 4 = 180

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Finding the equation from a graph Y= 2sin(2t + ) + 4 Phase shift = x time for mean line = 2 Phase shift = 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 = –90

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

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

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Finding the equation from a graph

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