Question

A sinusoidal function whose period is π/2, maximum value is 10, and minimum value is −4 has a y-intercept of 10.What is the equation of the function described?

Answer 1

The general equation for the sinusoidal function is:

`y=a\sin (bx)+h`

Where:

a is the amplitude

b = 2π/period

h is the vertical shift

Given:

period = π/2

So,

`b=(2\pi)/((\pi)/(2))=4`

the maximum value is 10, and the minimum value is −4

so, the amplitude will be:

`a=(1)/(2)\cdot(10-(-4))=(1)/(2)\cdot14=7`

The y-intercept of 10

so, the vertical shift will be:

`h=10-7=3`

Now, the function will be sin or cos

As the y-intercept = 10

So, when x = 0, y = 10

So, the function will be:

`f(x)=7\cos (4x)+3`