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Grade 12 Advanced Functions

1. The cyclical pattern of symptoms in a patient is sinusoidal in nature. When graphed as a function of intensity, g(x), and time, x in months, the function is very similar to f(x)= sin x. Intensity is ranked on a scale of 0-a, where zero represents normal (min) and ‘a’ represents full-blown symptoms(max). The amplitude of the cyclical pattern is a/2 and the equation of the axis of the curve is y=a/2.
The period of the function is a/4 months. Using f(x)= sin x as a base function, the function of the symptoms has been horizontally translated a/8 months to the right.
a. Write a possible equation for the function g(x).
b. State all the transformations of the trigonometry function.
c. Sketch a graph of the function g(x), by hand on the interval 0 <x< a/2 (use key points and the table to graph).

2. Particular areas of this cyclical pattern are noteworthy. Use the equation found in question one.
a.Determine algebraically when the patient first ranked his intensity at 0.75a.
b. Determine when the patient ranked his intensity at 0.75a for the third time. c. Determine algebraically how high the patient ranked the intensity at 12 months.


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  1. the period of sin(kx) is 2π/k
    They have told you the amplitude and vertical translation. You know it will look like
    y = A + Bcos(k(x-h))

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