Question

Question #e7f98

Answer 1

y = 3(1/4(x - 3`pi`/2)) - 4

Explanation:

Consider this skeleton equation:
y = a(bx + c) + d

Amplitude is the a value, so plug it in for a in the equation:
y = 3(bx + c) + d

With the period you can find the b value using this equation:
period = 2`pi`/b
(use 2`pi` for cos,sin,csc,sec functions & just `pi` for tan,cot fucntions)
Since you already know the period, plug it in to this equation and solve for b:
8`pi` = 2`pi`/b ---> b = 1/4
Now plug this b value into the skeleton equation:
y = 3(1/4(x + c)) + d

Phase shift of 3`pi`/2 means the graph shifts left, so it's the c value; now plug it into the equation:
y = 3(1/4(x - 3`pi`/2)) + d

Finally, the vertical shift of -4 is shifting the graph downward, which is the d value. Now plug it into the equation to get the final equation:
y = 3(1/4(x - 3`pi`/2)) - 4