Question

A sinusoidal function whose period is π/2 , maximum value is 10, and minimum value is −4 has a y-intercept of 3. What is the equation of the function described?

Answer 1

`f(\theta)=3+7sin(4\theta)`

Explanation:

The sinusoidal function has a general form of:

`f(\theta)=Y+Asin(k\theta)`

The period is given by:

`P=(2\pi)/(k)\\(\pi)/(2)= (2\pi)/(k)\\k=4`

Y is the y-intercept, thus y = 3.

At the maximum value:

`f(max) = Y+A\\10 = 3+A\\A=7`

At the minimum value:

`f(min) = Y-A\\-4 = 3-A\\A=7`

Therefore, the equation of the function described is:

`f(\theta)=3+7sin(4\theta)`