SOLUTION: https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/42c0ad0b-0f8d-3d07-9a3e-d73dbec1a86b___05921975-d63e-3ce2-b97a-4ae6252cdc71.png This was either a sin o

Algebra ->  Trigonometry-basics -> SOLUTION: https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/42c0ad0b-0f8d-3d07-9a3e-d73dbec1a86b___05921975-d63e-3ce2-b97a-4ae6252cdc71.png This was either a sin o      Log On


   

Question 1196054: https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/42c0ad0b-0f8d-3d07-9a3e-d73dbec1a86b___05921975-d63e-3ce2-b97a-4ae6252cdc71.png
This was either a sin or cos graph
Please find the function or equation of the graph
y = Asin(Bx-C)
y = Acos(Bx-C)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

I just solved several similar problems for you.

Now my question is: are you going to learn from my posts,
or you are a professional collector of solutions produced by others ?



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I'm not sure what is intended with this problem. There are an infinite number of sine and cosine functions that have the graph that is shown.

For simplicity, I will ignore the amplitude and period of the graph that is shown, using an amplitude of 1 and a period of 2pi, and show that there are many different functions that have the same graph.

In the graph that is shown, the function value at x=0 is zero and decreasing. So it could be a sine function with no horizontal shift and A negative: y=-sin%28x%29

graph%28400%2C100%2C-pi%2C3pi%2C-2%2C2%2C-sin%28x%29%29

It could also be a sine function shifted pi to the right, with A positive: y=sin%28x-pi%29

graph%28400%2C100%2C-pi%2C3pi%2C-2%2C2%2Csin%28x-pi%29%29

Note that you would get the same graph if it were a sine function shifted pi to the left: y=sin%28x%2Bpi%29

graph%28400%2C100%2C-pi%2C3pi%2C-2%2C2%2Csin%28x%2Bpi%29%29

It could also be a cosine function, with A positive and shifted pi/2 to the left (or 3pi/2 to the right): y=cos%28x%2Bpi%2F2%29

graph%28400%2C100%2C-pi%2C3pi%2C-2%2C2%2Ccos%28x%2Bpi%2F2%29%29

Finally, it could be a cosine function with A negative and shifted pi/2 to the right: y=-cos%28x-pi%2F2%29

graph%28400%2C100%2C-pi%2C3pi%2C-2%2C2%2C-cos%28x-pi%2F2%29%29

The graphs of all those functions are the same; and there are an infinite number of other sine and cosine function with the same graph, just using different horizontal shifts.

The way the problem is stated, it appears that there is only one right answer; but that is clearly not the case.