Amplitude and Period (1 Viewer)

[Kutay]

Hey i was wondering whats the formula to get the amplitude and the period formula

 

[Kutay]

its for the question 2cos3x = 1
its really annoying me when i can't get a question

 

[FinalFantasy]

x=asin nt
a=amplitude
T(period)=2pi\n

for 2cos3x = 1
a=2 , T=2pi\3

 

[Slidey]

cosx has period 2pi, amplitude: 1
cos3x has period 2pi/3, amplitude: 1
2cos3x has period 2pi/3, amplitude: 2

 

[FinalFantasy]

hey captain! y u keep changing avatar??

 

[Slidey]

I have no idea. But I like this one.

 

[Trev]

why do u call him captain? whenever you say that i get foncused thinking your talking to 'Captain pi'

 

[FinalFantasy]

hahaha, well slide rule is captain to me, why? bcoz i was talking to him before and i called him captain for some reason

 

[Trev]

fool.......

 

[zenger69]

if y=a sin bx (replace sin with any trig ratio)

a is the amplitude

period is given by 2pi/b EXCEPT TAN which is pi/b.

If you want to sketch that 2cos3x=1 (put it all to 1 side)

2cos3x-1=0

Firstly draw the cos graph regardless of it's amplitude.
Then put in the x values (such as pi/2, 3pi/2 etc etc etc)
Then move your amplitude down 1 unit. So instead of between 2 and -2 the graph is between 1 and -3.

If i'm wrong please correct me.
Hope it helps

 

[|Axis_]

It doesn't make sense (to me at least!) to talk about "amplitude" or "period" of 2cos3x=1 even though I suppose I know what you mean (see 3rd post by FinalFantasy).

By some of the reasoning given above, 2cos3x=1 would have an "amplitude" of 2; yet cos3x=1/2, which is the same, would apparently have an "amplitude" of 1. Contradiction.

The solutions to 2cos3x=1 are points on a number line for the variable x. The points are the x values of where the graphs of, say, y=2cos3x and y=1 coincide (or where y=cos3x and y=1/2 coincide, or where y=2cos3x-1 and y=0 coincide, etc. All of these methods will yield the same solutions).

To systematically find the solutions of x without graphing:
2cos3x = 1
is cos3x = 1/2

Now recalling "All stations to Central" mnemonic from kindy, we carefully note that the angle 3x lies in the 1st or 4th quadrant.
3x = +- arccos(1/2) + 2n(pi) , integer n
x = +- (1/3)arccos(1/2) + (2/3)n(pi)

Correct me if I'm wrong - bit rusty coz of the summer hol.


By the way, it might be useful to remember this:
---------------------------------------
For f(x) = M+Acos(Bx+C) = M+Acos[B(x+C/B)]

the graph of y=f(x) is like the cos graph you know, except that:

Amplitude = |A|
Period = |2pi/B|
The graph is shifted up by M (or down if M is negative)
The graph if shifted left by C/B (or right if C/B is negative)
If A is negative then remeber that the shape of the graph is like upside-down cos.
----------------------------------------

phew

 

[FinalFantasy]

for 2cos3x = 1
i took "1" as the "x" in x=asin nt where x is center of motion
da person hasn't stated what that 1 was at first, so 2cos3x = 1 can be interpreted in different ways=P

 

[goan_crazy]

is this 2 unit...crap i have never seen this b4
what topic is it?
we prob havent done it

 

[...]

sounds more like 3u to me

 

[Slidey]

It is 2 unit.

 

[Trev]

what topic is amplitude and period in? please tell me its not in a topic ive done yet

 

[|Axis_]

for 2cos3x = 1
i took "1" as the "x" in x=asin nt where x is center of motion
da person hasn't stated what that 1 was at first, so 2cos3x = 1 can be interpreted in different ways=P

You know I didn't mean to pick on you FinalFantasy. I was just saying, y'know..

 

[FinalFantasy]

hahaha, i don't mind at all... i like to be rectified if i get stuff wrong

 

[Will_Sparky]

what topic is amplitude and period in? please tell me its not in a topic ive done yet

Applications of Calculas To The Physical World... if I'm not mistaking.

 

[withoutaface]

Probably also the trig functions topic.