The graph to the right is a function of the form y = A sin (Bx - C) D, B > 0. Th

Question

The graph to the right is a function of the form y = A sin (Bx - C) D, B > 0. The five quarter points of one cycle of the graph, from left to right, are given below. These five y quarter points on the graph correspond to the five quarter points on the graph of y - sin x over the interval [0,2pi]. Determine the equation of the specific function that is 2 represented by the given graph based on the association of the labeled quarter points and the quarter points of the graph of y = sin x over the interval [0,2pi].

Explanation / Answer

Eight quarter points make one cycle corresponding to 2pi

So, 4 quarter points correspond to half cycle : 4pi/3 - (-pi/6) = 3pi/2

a )Time period = 2* 3pi/2 = 3pi

b) Time period = 2pi/B ; 3pi = 2pi/B

B = 2/3

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