Maximum value

[Mandsi]

[FONT=verdana, geneva, lucida, lucida grande, arial, helvetica, sans-serif]Got an interesting question from the teacher at school a few days ago and i still can't make any sense out of it.

[/FONT]Find the maximum displacement of the oscillation

x=2cos(wt) +cos[wt-(π /6)]

We have been taught that the typical trigonometric expression goes like this -->eg. A sin (BX+C) + D
where the amplitude is A, period is 2π/B, phase angle is C, phase shift is C/B and vertical shift is D.

But then again i can't seem to apply this in the above mentioned question..... Would appreciate if anyone can enlighten me.

 

[Deleted member 4993]

Got an interesting question from the teacher at school a few days ago and i still can't make any sense out of it.

Find the maximum displacement of the oscillation

x=2cos(wt) +cos[wt-(π /6)]

We have been taught that the typical trigonometric expression goes like this -->eg. A sin (BX+C) + D
where the amplitude is A, period is 2π/B, phase angle is C, phase shift is C/B and vertical shift is D.

But then again i can't seem to apply this in the above mentioned question..... Would appreciate if anyone can enlighten me.

Do you know how to calculate the maximum of a single variable function?

 

[Ishuda]

Got an interesting question from the teacher at school a few days ago and i still can't make any sense out of it.

Find the maximum displacement of the oscillation

x=2cos(wt) +cos[wt-(π /6)]

We have been taught that the typical trigonometric expression goes like this -->eg. A sin (BX+C) + D
where the amplitude is A, period is 2π/B, phase angle is C, phase shift is C/B and vertical shift is D.

But then again i can't seem to apply this in the above mentioned question..... Would appreciate if anyone can enlighten me.

Since this is under Geometry and Trig, I would assume you wouldn't use derivatives to find the extrema. Also, since the two cosine functions have the same period, the sum can be reduced to a single cosine [or sine] function. First note that if we have a function
x = A sin(t) + B cos(t)
where A and B are not both zero, we can turn it into a single cosine [or sine] function in the following manner:
Let
cos(c) = A/(A² + B²)^1/2
sin(c) = B/(A² + B²)^1/2
Then we can write x as
x = (A² + B²)^1/2 [sin(t) cos(c) + cos(t) sin(c)] = (A² + B²)^1/2 sin(t+c)
Notice that if I had swapped definitions for sin(c) and cos(c), I would have gotten a cosine function.

Now, for your problem, let
s = wt - π /12
and get
t = s + π /12
and
t - π /6 = s - π /12
Now expand out the two cosine functions in
x = 2 cos(s + π /12) + cos(s - π /12)
to get
x = A sin(s) + B cos(s)
If you do that, it should get you on your way.