1. Sinusoidal Help?

Determine the values of a and d in the sinusoidal function

y=asin(bx+c) +d

if the maximum value is 12 and the minimum value is 4.

Find the value of b in the sinusoidal function if the period is 5.

That is what I'm being asked. And yet again the crappy online course hasn't even mentioned it.

2. Originally Posted by MathIsRelativelyUseless
Determine the values of a and d in the sinusoidal function

y=asin(bx+c) +d

if the maximum value is 12 and the minimum value is 4.

Find the value of b in the sinusoidal function if the period is 5.

That is what I'm being asked. And yet again the crappy online course hasn't even mentioned it.
First part:

Ok, for this you need to know that $\sin{(bx+c)}$ ranges from -1 to 1. You are given that the minimum value of y is 4 and the maximum value of y is 12. Since the sine function is the only value of the function that is going to be changing, this is a relatively easy problem to solve. When the sine is at its least, the function will be at its least. So when the sine is -1, the function is 4. Similarly, when the sine is at its greatest, the function will be at its greatest. So when the sine is 1, the function is 12. Hence we have:
$4 = -a + d$
$12 = a + d$
$16 = 2d$
$d = 8, a = 4$.
To find b, note that the period of the sin function (without being modified by b) is $2\pi$. The period is therefore going to be equal to $\frac{2\pi}{b}$. So you just need to solve the equation $\frac{2\pi}{b} = 5$.