Determine an equation if the given base graph has been transformed as follows. siny x= compressed vertically by a factor of3 1 , reflected in the x-axis, translated120 to the right, and 5.5 units upward.

1. For each of the following: determine if the graph is periodic, and if it is periodic state the period and the amplitude.
Periodic (Y/N): Periodic (Y/N):
if periodic: if periodic:
Period: Period:
Amplitude: Amplitude:

2. Determine an equation if the given base graph has been transformed as follows. (4marks)
.siny x= compressed vertically by a factor of3 1 , reflected in the x–axis, translated120 to the right, and 5.5 units upward.
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3. For the function, state the following. (4)( ) 25.42430sin4 −+= xy phase shift____________________ period ______ vertical displacement ____________________ amplitude ______ range ____________________
5. Determine: amplitude, horizontal and vertical phase shift, period ( 4)

6. If the base graph issiny x= describe, in words, the transformations that occur to . (3)
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Application
7. For each function, state the following, draw a sketch, then graph.. (10)
a. p.s._______________ per. ____ v.d. _______________ amp. ____ range
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b.( ) 2150sin2 ++= xy p.s._______________ per.____ v. d._____________ amp.____ range_________

8. A radio transmission tower sways in a strong wind so that the top moves back and forth as much as 56 cm with a period of 6.0 s. This motion can be modeled using a sine function. (7 marks)
a) Sketch a graph of the sideways displacement of the tower, d, from its normal position as a function of time, t, for 12.0 s. 
b) Graph it the function (hint: you need to find amplitude, period, h shift, axis of the curve if they apply to your graph) 

9. The height of a rider on a Ferris wheel, in metres, can be modelled by the function h(x) = 9 sin(x − 90)+ 10 ,where x is the rotation angle, in degrees, that you’re on the ride. (5)
a. What is your maximum height on the Ferris wheel?
b. What is your minimum height on the Ferris wheel?
c. How far off the ground is the centre of the Ferris wheel?
d. What is the radius of the Ferris wheel?
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