Trigonometry

Question

Help with trigonometry
To get a better look at the graph, you can click on it.The curve above is the graph of a sinusoidal function. It goes through the points (−7,−3)  and (3,−3)  . Find a sinusoidal function that matches the given graph. If needed, you can enter π  =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.
 
https://webwork.latech.edu/webwork2_files/tmp/Winter201516-Math240-Walters//gif/gvr001-2631-setstewart7e_ch05s03prob12image1.png
 
Please explain the process to me. Thanks in advance.

Answer 1

I can't read it, but if the two points are beginning and end, both minimums with average = 0, then the period = 2pi/B 10

and B = 2pi/10 = pi/5

general formula is Asin(x(B-C)+ D

A = Amplitude = (max-min)/2= (3--3)/2= 3

B= pi/5

C = 0 = phase shift

d = 0

f(x) = 3sin(pix/5)

that's the most simple sinusoidal function

= about 3sin.6708x