3) The cyclical pattern of symptoms is sinusoidal in nature. When graphed as a function of intensity, g(x), and time, x in months, the function was very similar to f(x) = sin x. Dr. Philips described the shape of this graph, with reference to f(x) = sin x. Intensity is ranked on a scale of 0-10, where zero represents normal and ten represents full blown symptoms. The amplitude of the cyclical pattern is 5 and the equation of the axis of the curve is y = 5 . The period of the function is 4 months. Using f(x)= sin x as a base function, the symptoms function has been horizontally translated 2 months to the right. Write a possible equation for the function g(x). b) Sketch a graph of the function g(x), by hand, on the interval 0sxs18 10 ... 4. 10 11 12 13 14 15 16 17 18 19

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 76 degrees at midnight and the high temperature is 86, at 6pm, while the low is 66 degrees, at 6am. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.D(t) =

Sketch a graph of the function g(x)=-2sin(1/4x - pi/4)+1. Be sure to label the scale on the axes and draw at least two cycles.