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

Answer:

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

Step-by-step explanation:

The sinusoidal function has a general form of:

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

The period is given by:

$P=\frac{2\pi}{k}\\\frac{\pi}{2}= \frac{2\pi}{k}\\k=4$

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:

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