Suppose 𝑓(𝑥) is a function whose graph is a sinusoid with the following features 1. Amplitude = −5 2. Period = 𝜋5 3. Phase shift = 𝜋−40 4. Midline 𝑦=5.

Question

Find an equation for the graph of f(x). I can not figure this one out even after asking my teacher, and I have about five more of these I need to learn how to do step by step.

Answer 1

general equation is

f(x) = Asin(B(x+C)) + D

where A= amplitude, 360/B or 2pi/B = period, C is the horizontal shift, D is the vertical shift

2pi/B = pi/5

2/B=1/5

B =2(5) =10

so, A= -5/2, B=10, C=pi/-40, D=5

f(x) = -(5/2)sin(10(x-pi/40)) + 5