Question 1125441
the general formula for the sine wave is shown in the following link.


<a href = "https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html" target = "_blank">https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html</a>


the formula shown in the link is y = A * sin(B * (x - C) ) + D


A is the amplitude.
B is the frequency.
C is the horizontal shift.
D is the vertical shift.


in your problem, what they call A, you call p, and what they call B, you call a.


the amplitude is 3, therefore p = 3.


the period is 180 degrees.


this means that the number of degrees for the sine wave to make one complete cycle is 180 degrees.


the formula for period is p = 360 / f, and the formula for frequency is f = 360 / p.


you are given that the period is 180 degrees.


to find the frequency, use the formula for f = 360 / p.


that becomes f = 360 / 180 = 2.


the frequency is 2, which is the value of the variable a in your problem (called B in the reference).


your formula then becomes y = 3 * sin(2 * x).


here's the graph.


<img src = "http://theo.x10hosting.com/2018/100701.jpg" alt="$$$" >


from the graph, you can see thqt the turning point is at (135 degrees, -3).


the period is 180 degrees and the amplitude is 3.


an amplitude of 3 means the graph goes plus or minus 3 units from the denter line.


the center line of this graph is at y = 0.


the blue line is the graph.


the orange line is used so that i can show the intersection of the graph with the value of x = 135 degrees.


the orange shading is used to frame the 180 degree cycle of the sine wave.