maths question?

Question

for the function defined as f(t)=10cos(4Πt-1), find the amplitude,phase angle angular velocity and frequency. find also the first positive value of t when the function equals 5

i have managed to do this

f(t)=10cos(4Πt-1)
amplitude = 10
phase angle = -1
angular velocity = 4Π
frequency = 0.5 hz

10cos(4Πt-1)=5
=> cos(4Πt-1)=0.5
=> 4Πt-1 = 1.047 i dont know why the value is this could someone explain?

Answer 1

ask in physics section also u may get ur answer more perfectly there.

Answer 2

For Philo:

No, 1/4π is the time at which the function would 'act' as it would at t=0 if there were no phase shift.

And, BTW, the phase is +1, not -1. The canonical form of the equation is

f(t) = Acos(2πft-Φ)

where

A = amplitude
f = frequency (in this case 2 Hz.)
Φ = phase angle

A positive Φ shifts the function to the 'right' and a negative Φ shifts it to the 'left' (in keeping with the sign convention along the horizontal axis)


Doug

Answer 3

x=2

Answer 4

You have cos(4πt-1) = .5, and you should know cos(π/3) = .5, {π/3 = 1.047 by the way}

4πt - 1 = π/3 (plus multiples of 2π), that is
4πt - 1 = π/3 + 2kπ
4πt = 1 + π/3 + 2kπ
t = 1/(4π) + 1/12 + k/2
t = 0.1629 + 0.5k

When k=0, smallest positive value of t is 0.1629.

Where do you get phase angle = -1? Normally cos(t) = 1 when t = 0. But cos(4πt-1) = 1 when 4πt-1 = 0, when t = 1/(4π). Isn't THAT your phase angle?

Answer 5

Right:
The function equals 5 so:
5=10*cos(4*Pi*t -1)
0.5=cos(4*Pi*t -1)

Now u need to take arc-cos of both sides of the equation, but it matters which units the angles are measured in (degrees or radians)

acos(0.5) = 60 degrees = 1.047 radians

Once you're this far, the rest is just algebra.

Answer 6

There isn't really a why.
Assuming the last line of your calculation is correct, then: -

t = 0.162895...
=> Angular velocity = 4*Pi*t = 2.047 radians per second (if t is in seconds)

Additional: -

Oh dear. Philo's answer is dredging up some nasty memories. I'm pretty sure he's on to the methodology for solving this, but I couldn't vouch for his answer. I'm away to do some serious revision now. See you in a couple of months.

Answer 7

u have to compare the equation with
f(t)=Asin(wt+phase angle)
and not
f(t)=Acos(wt+phase angle)
so convert the cos term to sine term before comparing and then try....

Answer 8

(4.pi.t-1) does equal 1.047 if you use RADIANS
da da !

Answer 9

thats gone well over my head

Answer 10

why don't you better stop thinking of maths and start doing something interesting