Question 1196054
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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.<br>
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.<br>
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(x)}}}<br>
{{{graph(400,100,-pi,3pi,-2,2,-sin(x))}}}<br>
It could also be a sine function shifted pi to the right, with A positive: {{{y=sin(x-pi)}}}<br>
{{{graph(400,100,-pi,3pi,-2,2,sin(x-pi))}}}<br>
Note that you would get the same graph if it were a sine function shifted pi to the left: {{{y=sin(x+pi)}}}<br>
{{{graph(400,100,-pi,3pi,-2,2,sin(x+pi))}}}<br>
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(x+pi/2)}}}<br>
{{{graph(400,100,-pi,3pi,-2,2,cos(x+pi/2))}}}<br>
Finally, it could be a cosine function with A negative and shifted pi/2 to the right: {{{y=-cos(x-pi/2)}}}<br>
{{{graph(400,100,-pi,3pi,-2,2,-cos(x-pi/2))}}}<br>
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.<br>
The way the problem is stated, it appears that there is only one right answer; but that is clearly not the case.<br>