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,

$b=\frac{2\pi}{\frac{\pi}{2}}=4$

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

so, the amplitude will be:

$a=\frac{1}{2}\cdot(10-(-4))=\frac{1}{2}\cdot14=7$

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:

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