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Each trig function repeats every cycle. If we take sin(x) as an example, the graph of sin(x) oscillates as sin(x) starts at 0 and when x=2π radians sin(x) becomes zero again, and it’s the same for the other trig functions.

Since x is a measure of distance we can express x in terms of time, x=vt where v is a constant velocity (of the sine wave). When the wavelength x=2π, vt=2π so t=2π/v. This is the time it takes to complete a cycle. The inverse of t is the frequency, the number of cycles in unit time. So f, the frequency, is v/2π=153.85. From this we can find v=307.7π and the sine function becomes sin(307.7πt). When t=0 we have the start of the cycle, and when 307.7πt=2π we have the end of the cycle when t=2/307.7=1/153.85. This is about 0.0065 time units (seconds). If we plot the graph of f(x)=trig(307.7πt) where trig is any of the trig functions, and t is in seconds, we will see there are 153.85 oscillations in unit time (one second).

Another way to look at this is to use the wavelength x. Wavelength × frequency = velocity, so x=v/f and we could have looked at sin(x) where x=0 and x=2π=v/153.85. Again, v=307.7π m/s where x is measured in metres. 

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