Question

what is the equation for the graphs given the following information:

2. the graph of: y = asinbx has amplitude of 4 and a period of pi/6

3. a sinusoid graph with a maximum at A(0,3) and a minimum at (2pi, -3)

Answer 1

there are lots of online graphing sites: wolframalpha and desmos are two

#2. sin(kx) has a period of 2pi/k
so, a period of pi/6 means 2pi/k = pi/6 ==> k=12
y = 4sin(12x)

#3.
y varies from -3 to 3, so a = 3
max to min is 1/2 period, so you have a period of 4pi
cosine starts at a maximum, so
y = 3 cos(x/2)