The curve above is the graph of a sinusoidal function It goe

The curve above is the graph of a sinusoidal function. It goes through the points (-5, -2) and (1, -2). Find a sinusoidal function that matches the given graph. If needed, you can enter pi = 3.1416... as \'pi\' in your answer, otherwise use at least 3 decimal digits. f(x) =

Solution

y = Asin(B(x-C) +D

Period = 4 - (-2) = 6

B = 2pi/6 = pi/3

So, A +D = 2 ---(1)

-A +D = -2 ---(2)

We get D =0 ; A = 2

amplitude A = 2

y = 2sin(pi/3(x - C)

It passes through ( -5 ,-2)

-2 = 2sin(-5pi/3 -pi*C/3)

3pi/2 = -5pi/3 - pi*C/3

19pi/6 = -pi*C/3

C = - 19/2

So, y = 2sin(pi/3( x +19/2)