how do i make a sinusodial equation with amplitude, period etc...?

Question

I would like to make a sinusodial equation in the form y=a*sin(bx+c)+d and dont know how to make it. I have the following information :
median=0
amplitude=160
period=1/60
start point=(0,0)

Answer 1

The only thing that might give you trouble here is period, which is the time to complete one cycle, or revolution. One revolution is 2π radians. The median of any sinusoidal over 1 period is 0, so d=0 in your equation.
Amplitude of 160 requires a = 160
Period of 1/60 requires that b = 2π/(1/60) = 120π
Your starting point is (0,0) so you need to choose a sine function with c = 0 or a cosine function with c = -π/2

y = 160sin(120πx) = 160cos(120πx - π/2)

If you prefer to use degrees, 2π becomes 360, and your equation(s) become

y = 160sin(21600x) = 160cos(21600x - 90)

Answer 2

The definitions of the various parameters of the general sinusoidal equation
y=a*sin(bx+c)+d are;

a : amplitude of the sinusoidal wave
b: frequency (angular frequency to be precise)
c: phase shift (or initial phase)
d: a constant that depends on the starting value of y and the phase shift

In order to solve your problem I have to assume that the period of this particular sinusoidal wave is given in seconds. According to the above definitions it follows;
a = 160

The frequency and the period are related to each other through the equation
frequency = (2*Pi) / period.
Therefore b 120*Pi

Since median = 0 the line of propagation of the wave coincides with the x-axis. With that and since y = 0 and x= 0 at the start we can deduce that d = 0 and c = 0.

Therefore the equation is y = 160*Sin(120*Pi*x)

Answer 3

a = 160, amplitude
b(1/60) = 2π
Solve for b, b = 120 π
0 = a sin(c),
Solve for c, c = n π, where n is any integer.
By the way, median = 0 is automatically matched for a whole period, if d = 0.

Therefore,
y = 160 sin(120 π x + n π)

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I put c = n π instead of c = 0 because the sinusoidal equation is not unique. For example, if f(x) is decreasing at x = 0, then we can pick n = 1 to match the condition: y = 160 sin(120 π x + π)

Answer 4

Just type waves or electromagnetic radiation into Wikipedia and you'll get enough material to write several papers.