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

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

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

4. 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

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

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

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

8. 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

9. 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

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

11. 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

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

13. Finding the equation from a graph
Y= 2sin(t+ ) + 4
180
The period = 180
 =

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

15. 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

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

17. 2Sin(x+45)
Sin(x+30)
2Sin(x+60)+1
Sin(x-15)+2

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

19. Finding the equation from a graph