The current in an electrical circuit is given by i=5 sin?[120?(t-1/240)] where i

Question

The current in an electrical circuit is given by i=5 sin?[120?(t-1/240)] where i is measured in amperes and t is seconds. State the amplitude, period, and phase shift and then graph this equation.

Explanation / Answer

It may help you a lot Amplitude = - 3 factor 2 from 2x out : y= - sin2(x+Pi/4) period = 2Pi/2 = Pi and phase shift = - Pi/4 solve 0=-3sin2(x+Pi/4) so 2(x+Pi/4)=0 => x=Pi/4 OR I like to write my sine and cosine functions in this form. y = a sin[b(x-c)] + d In this form, |a| = amplitude (how high and low the graph will go) c = phase shift (how much the graph is moved left or right) d = vertical shift ( how much the graph is moved up or down) 2pi / b = period (the length it takes the graph to make one cycle) You didn't put a variable in your equation. I'm assuming that's a typo. I'll just change the problem a bit so I can at least give you an example. Instead of 40, I'll just put 4x. y = -2 sin(4x + 2pi) It's almost in the form I showed you, but you can't have anything being directly multiplied to the x, so I'll factor a 4 out. y = -2 sin[4(x + pi/2)] If you want it to look exactly like the formula I gave, do this y = -2 sin[4(x - (-pi/2)] So, a = -2 b = 4 c = -pi/2 d = 0 amplitude = |a| = |-2| = 2 period = 2pi / b = 2pi / 4 = pi / 2 phase shift = -pi/2. This means the graph has a horizontal shift of pi/2 units to the left. Hope this clears up any problems you're having.

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