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Sinusoidal Function Transformations

1. Below is the graph of a sinusoidal function, with angles measured in degrees.

1 a)

What is the domain of the function?

1 b)

What is the range of the function? Then what is the amplitude?

1 c)

What is the period of the function? [Don't forget the units.]

1 d)

What is the axis of the curve of the function? (i.e. the horizontal line halfway between the max and the min)

1 e)

What is the phase shift of the function? Did you compare to the sine or cosine function? [Make sure to use "right" or "left" in your answer.]

1 f)

State the equation of the function in the form or .

2. Describing the properties of a sinusoidal function given its equation.

The height of the tide in a small beach town is measured along a seawall. The equation  describes the height of the tide in meters at time in hours.
Image

2 a)

What is the range and domain of the function?

2 b)

What is the amplitude of the function?

2 c)

What is the period of the function?

2 d)

What is the phase shift of the function?

3. Describing the average monthly temperature using sinusoidal functions.

The average monthly temperature (in C) in London, ON can be described by a sinusoidal function. The temperature fluctuates between C and C. Representing January as , February as , and so on; the phase shift of the function is 4 months right. The average temperature is hottest in July.

3 a)

What is the equation of the sinusoidal function that models the average monthly temperature in London, ON? State it as where is the month as described above.

4. a) Follow the step below to model the support railing (diagonal beams) with the sine curve.

4. b)

Which variables () do the sliders 1 to 4 correspond with in the following equation of a sine function: ?

4. c)

Which property of a sine curve (e.g. amplitude, period, axis of curve, phase shift) does each slider affect?