Question 1140909
i believe your equation is y = 2 * sin ( 60 * ( x - 1.5 ) ) when you are working in degrees.


it looks like this:


<img src= "http://theo.x10hosting.com/2019/051501.jpg" alt="$$$" >


i believe your equation is y = 2 * sin ( pi/3 *(x - 3/2 ) ) when you are working in radians.


<img src = "http://theo.x10hosting.com/2019/051502.jpg" alt="$$$" >


you will notice that both graphs have a period of 6 and that both graphs are identical to each other.


y represents the position of the pistons which represents p for graphing purposes.


x represents time, which represents the variable t for graphing purposes.


in other words, the identical equations are:


p = 2 * sin ( 60 * ( t - 1.5 ) ) when you are working in degrees and .....


p = 2 * sin ( pi/3 *(t - 3/2 ) ) when you are working radians.


the biggest problem i had with this was the horizontal shift.


the first equation i worked was in degrees.


the phase shift to the left was given as pi / 2.


that's in radians.


i converted it to degrees by multiplying it by 180 / pi.


pi / 2 * 180 / pi  = 90 degrees.


that, i believe, is the phase shift if the periods was the normal period of 360 degrees.


i then needed to convert that phase shift to when the frequency was 60 rather than 1.


that made the phase shift equal to 90 / 60 = 1.5.


the amplitude was set at 2.


the period was set at 6.


the frequency was 360 / 6 = 60.


that led to the equation you see on the first graph.


when working in radians, ......


the amplitude was still 2.


the period was still 6.


the frequency became 2 * pi / 6 = 2/6 * pi = pi / 3.


the phase shift became (pi / 2) / (pi / 3) which became (pi / 2) * (3 / pi)  which became 3 / 2.


that's the same as 2.5, even though i left it at 3 / 2.


that led to the equation you see on the second graph.


i had a hell of a time finding references to phase shift in relationship to frequency, but i think i got a hint from the following reference.


<a href = "https://www.mathway.com/examples/trigonometry/graphing-trigonometric-functions/amplitude-period-and-phase-shift?id=342" target = "_blank">https://www.mathway.com/examples/trigonometry/graphing-trigonometric-functions/amplitude-period-and-phase-shift?id=342</a>


what this is saying is, i think, .....


formula is y = sin ( 60 * x + 90) which is then translated to:


y = sin (60 * (x + 90 / 60) which then becomes y = sin (60 * (x + 1.5)


the shifting rules are:


if the shift is to the left, then it's x + c.


if the shift is to the right, then it's x - c.


this was probably the most confusing part for me and i hope that i got it right.


the degree formula just didn't work when i did it any other way.


this way, both the degree formula and the radian formula give the same answer which is a pretty good clue that it's probably right.