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?

Question

asked Jul 1, 2021 222k views

1 Answer

Safarov · Answer 1 · 2021-07-05T16:50:06+0000

Answer:

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

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:

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