# Phase angle leading or lagging

#### Sanctuary10

Joined Oct 4, 2020
8
Hi all, a little help would be great about stating if a phase angle is leading or lagging.

Using one of the questions I've done as an example.

Y=5sin4t - Find frequency, period, amplitude and phase angle.
My results
>0.64Hz
>1.5s
>5
>0°

What I don't quite understand is whether the phase angle is leading or lagging? (if my answer is correct)
A number of the questions I've done result with 0° phase angle. Advance apologies if this is a stupid question.

Thanks

#### crutschow

Joined Mar 14, 2008
29,521
A phase angle only has meaning if it's with respect to another sinewave.
Here I see only one sinewave.

#### wayneh

Joined Sep 9, 2010
17,167
Advance apologies if this is a stupid question.
Well it's a little stupid in that it's like asking if one spot of your bike tire is ahead or behind some other spot. The answer is yes, it's both ahead and behind. It's a circle.

But there may be some convention to follow.

#### MrAl

Joined Jun 17, 2014
8,874
A phase angle only has meaning if it's with respect to another sinewave.
Here I see only one sinewave.
So by that description then i guess for the following:
V(t)=5*sin(t+pi/8)

i guess the phase shift pi/8 has no meaning? In cases where there is only one sine wave the phase shift is often taken to be relative to a sine wave with 0 degrees phase shift.
So the "phase" of that V(t) above is pi/8.

• Wolframore

#### MrAl

Joined Jun 17, 2014
8,874
Hi all, a little help would be great about stating if a phase angle is leading or lagging.

Using one of the questions I've done as an example.

Y=5sin4t - Find frequency, period, amplitude and phase angle.
My results
>0.64Hz
>1.5s
>5
>0°

What I don't quite understand is whether the phase angle is leading or lagging? (if my answer is correct)
A number of the questions I've done result with 0° phase angle. Advance apologies if this is a stupid question.

Thanks
If you plot two sine waves and one happens before the other in time it is leading, but if it is behind the other it is lagging. if you have only one sine wave then the phase is usually taken to be relative to a sine wave with phase shift of zero. That is because a general sine wave is:
A*sin(w*t+ph)
where ph is the phase shift angle in radians.

Now for your problem the phase shift is 0 as you have found, so what can you say about that relative to a sine wave at zero degrees or zero radians (either)?

• Wolframore

#### Wolframore

Joined Jan 21, 2019
2,533
As MrAl explained the phase shift is in the (t+phi) notation. A sine wave without any value for phi has zero phase shift. Further a DC shift can be notated after this portion:

Asin(4(t+phi)+B