Question

The function graphed is of the form y=a sin bx or y=a cos bx, where b>0. Determine the equation of the graph.

Answer 1

Since for x = 0 the equation is different from 0, we can conclude that the equation has the form of:

`y=a\cos (bx)`

Where:

a = Amplitude

b = Angular frequency

The angular frequency is:

`b=(2\pi)/(T)`

Where:

T = Period

From the graph the period is:

`\begin{gathered} T=4\pi \\ so\colon \\ b=(2\pi)/(4\pi) \\ b=(1)/(2) \end{gathered}`

Since the minimum value of the function is -4 we can conclude that the amplitude is 4, but the function is negative since it is reflected across the x-axis, therefore, the equation of the function is:

`y=-4\cos ((1)/(2)x)`