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in other words:
cos(0) = 1
cos(2pi) = 1
cos(4pi) = 1
cos(6pi) = 1
see a pattern?

6?

6 is the amplitude, yes.
What's the period.

any time James

i dont understand the period

cos(a x)
any thing in front of x , in this case
divide
period= 2pi/a
so cos(2 x)
period = 2pi/2 = pi

As eyust noted above,
cos(0) = 1
cos(2pi) = 1
cos(4pi) = 1
cos(6pi) = 1
So what is T?

i.e., what is the period for the function g(x) = cos(x)?

ooh i think i understand now

lets say for y(x)=-2cos4x the period would be 2pi?

No.

OMG this is hard!

No, it's just new for you. Do it a few more times and it'll be easy for you.

yes but that is very simple math lol

For me, the questions you're asking are also very simple.

but there was a time when they were new for me too. Just stick with it, and do a few more problems!

are you a math teacher?

Former University Lecturer

awesome

for y(x)=-2cos4x the amplitude is 2, correct?

Yes, the amplitude of y(x) = -2cos(4x) is 2, correct.

how do i find the frequency?

What's the definition of frequency, f?

the rate?

the rate of what?

of the wave

ooohh so the period of y(x)=-2cos4x is pi/2? because 2pi/4 is pi/2

yes.

omg yay lol

1? because 1/2 times 1 is 2

i mean 1 over 1/2 is 2

Yes, so f = 1/T. Or T = 1/f

T =period?

Yes T = period.

The lower the frequency, the higher the period.
The higher the frequency, the lower the period.

so if the period is pi/2, f=1/(pi/2)?

Yes. If T = pi/2, then f = 2/pi.

Which means every unit of time there are 2/pi complete oscillations.

got it :D

I have another problem :/ E(t)=110cos(120pit-pi/3)?

So you should know enough now to try and figure this out. First, what's the amplitude?

110

60?

Noo...

ooh no no no no sorry

If 120πT=2π, then T = ...

2pi/120pi

Simplify

pi/60pi=1/60=0.016666667

T = 1/60. Don't write the decimal expansion unless you really, really have to. Always messy.

yes i actually got it! aah thank you soooo much!

What is the frequency of E(t). What is the value of f for that function?

60

If the units of t are seconds, E(t) has a complete oscillation every 1/60 seconds.

alright

i think its 8 but im not sure