What are Lead and Lag Phases in Trigonometric Equations?

[krnhseya]

Homework Statement

Express the following as R sin (wt + alpha). Find R and alpha. This is lead phase.

Homework Equations

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The Attempt at a Solution

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I need to do same thing for cosine as well but the second part of problem asks you...

Lag phase instead of lead phase using cosine instead of sine...Also explain with words and sketches what lead and lag phase angles refer to.

This is an engineering course but it seems really simple. I tried to google, textbook, and etc. to find what this lead phase, lag phase, lead phase angle, and lag phase angle.
I am trying to finish most of my homework for upcoming week and this is driving me nuts!
Thank you!

 

[FrogPad]

Express what as a sin wave?

A sin wave either leads or lags another wave... so unless I am missing something, you need to put down some more information.

 

[krnhseya]

a) x = 4 cos (wt) + 10 sin (wt)
b) y = -2 cos (wt) + 5 sin (wt)

sorry about that and thank you for the response.

 

[Defennder]

Okay this looks like a maths and not engineering problem. Have you learned something called R-formula? You might have forgotten it, so I found a link via google to refresh your memory:

http://www.geocities.com/maths9233/Trigonometry/RFormula.html

As for lagging and leading phase, note that when you have expressed your trigo expressions in the required form there, alpha is what you would call the leading/lagging phase. When it is positive, it is leading, when negative it is lagging. But of course all this requires interpretation as to what exactly is leading and lagging, is it current, voltage or something else? It sounds as though you are made to calculate how much the current lags behind the voltage for a particular circuit setup.

 

[krnhseya]

Thanks for all the information.
No, it's not about the current, or anything...
Professor gave us what I wrote and it doesn't say what this is for...
I think it was given to just refresh our math skills or some sort, it's beginning of the semester so I have no clue how this will be used in future.
As far as angles are concerned, how they related to that form, R-formula?

I will have to study myself to get that R-formula from a) and b)...
Thanks again!

 

[Defennder]

Since you're doing engineering you'll sooner or later be aware (if you had done simple harmonic motion in your high school) that sine and cosine expressions don't always have to be of angles. wt, for example in your above 2 equations doesn't represent physically an angle of any kind. It is instead used as way of mathematically expressing a periodic function (one which oscillates between 2 values).

The point of R-formula is to allow you an easy way to add up two trigonometric expressions, and this 2 trigo expressions can mean anything in engineering. For eg. they can represent what happens when you add 2 waveforms due to either electrical signals, sound, etc. together to see what the resultant waveform is.

 

[krnhseya]

Yeah, I've done harmonic motion in high school and in university.
What I am wondering is that after I make an R formula, what's the angle in sketch and what it represents.
Yesterday when I was looking for it online, I found a document that had an angle but none of them matched my logic. (It had 30,45,60,90,120, etc.)

[edit]
I get...
1a) x=4coswt +10sinwt => x=10sinwt +4coswt => sqrt(116) sin (wt+arctan(4/10)) as a lead phase with R sin (wt + alpha) form
2a) x=4coswt +10sinwt => sqrt(116) cos (wt - arctan (10/4)) as a lag phase with R cos (wt + alpha) form.

For both b though...I don't get what I needed...
1b) y= -(2coswt-5sinwt) => sqrt(29) cos (wt + arctan 5/2) as a lead phase but it's not in sin form...
2b) y= 5sinwt-2coswt => sqrt(29) sin (wt - arctan 2/5) as a lag phase but it's not in cos form...

http://www.geocities.com/maths9233/Trigonometry/RFormula.html

I used that to solved it but I can't think of a way to switch cos to sin and sin to cos...

 

[krnhseya]

Is lead phase actually when alpha is positive? It seems like lead phase is when it's in terms of sin...ex) R sin (wt + alpha)
So for lag phase, R cos (wt + alpha)
Can anyone confirm this and how angles refer to this equation?
Thanks.