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Sine and cosine look similar, except they are out of phase. When we talk about sine and cosine as a function of time, the difference is called "lead" or "lag". Created by Willy McAllister.

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• At , cosine lags negative sine by 90 degree. Why don't we say cosine leads negative sine by 270 degree ?
• You can say that. Once you get the idea of "lead" and "lag" as it relates to the relative timing of sinusoids you can use the terms as you wish. The two statements you quoted are equivalent.
• At , why can't I say sine leads cosine by 90 degrees?

Why do we have to see the waves as if they are moving to the left?
• "Lead" and "Lag" reflect the relative timing of two signals. If func1 has a peak sooner than func2, we say func1 leads func2. In these graphs, time increases as you go to the right. So a time near the origin happens sooner than a time out to the right on the time axis.

If you look at the cosine function, it has its peak at t = 0.
The sine function has its peak at t = 90 degrees. That is later than the cosine peak.
So we say "cosine leads sine by 90", or equivalently, "sine lags cosine by 90".
• What is the phase difference between 3 phase AC sine waves and how can we calculate them?
• Hello Rajab,

The three phase are electrically offset from each other by 120°.

The mathematics for the calculations are not hard to do. Unfortunately, it can be hard to visualize the waveforms and keep track of what is happening. This is especially true of circuits involving reactive components (inductors and occasionally capacitors) and transformers.

There is an entire language electrical engineers master to handle these problems. If you are interested please take a look at phasors. Ref:

https://en.wikipedia.org/wiki/Phasor

Regards,

APD
• At you said that sin(theta) = cos(theta - 90)
but in textbooks I often see sin(theta) = cos(90 - theta).

I am pretty sure they are the same , but I am confused.
(1 vote)
• Your formula comes from the "complementary" angles inside a right triangle. The two angles other than the 90 angle are "complements" of each other. https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/sine-and-cosine-of-complementary-angles/a/sine-and-cosine-are-cofunctions.

The term "co sine" means "complement of sine".

In the video I used the negative of the angle:
theta - 90 = -(90 - theta)

This version of the formula gives the same answer. The reason is because cosine is an "even" function. It has symmetry about 0. Even means:
cos(theta) = cos(-theta)
cos(+45deg) = 0.707 = cos(-45deg)
cos(90 - theta) = cos(theta - 90) = sin(theta)

Whew, I thought you had me there for a second. Sine and Cosine are so similar they have symmetry every which way you look.
• Sir so what is the involvement of this AC circuit
(1 vote)
• why in inductor voltage leads the current?it is really hard for me to understand that what is going on.
(1 vote)
• in case of pure inductive circuit current lags behind voltage by 90' What actually happening physically due to which current is lagging?
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• The voltage across an inductor is highest when the slope of the current is greatest. If you assume the current is a sinewave, find the steepest part (where it crosses 0) and that's where the voltage will be the highest. If you plot out a bunch of other voltage points you will end up drawing another sinusoid that is 90 degrees out of phase.
(1 vote)
• I can't intuitively understand why a lead/lag would occur though. Maybe because i've been dealing with DC circuits for too long? I do understand that current and emf vary with time, but why would they be out of phase?
they each depend on each other and V=iR, so where is room for phase difference?
(1 vote)
• "They each depend on each other" ... very true.
"v = iR" ... also true --- for a RESISTOR.

For a capacitor that i-v dependence is different than a resistor,

i = C dv/dt ... for a capacitor the current depends on the slope of the voltage.

For an inductor the i-v dependence is different again,

v = L di/dt ... for an inductor the voltage depends on the slope of the current.

Exercise: Draw your favorite sinusoid (sine or cosine). Label that as the voltage on a Capacitor. Then, just by looking at your drawing, look at the slope of the voltage at every point and sketch in the current. The slope of voltage is zero at the top and bottom of the humps. The slope is greatest where the sinusoid crosses the time axis.

After you sketch current for one cycle, what does the current look like? (I hope you get a sinusoid with a 90 degree phase shift from the voltage.)

Do a similar exercise with the inductor equation. Start with a current sinusoid and derive the voltage.
(1 vote)