AC Voltage Waveform: Frequency, Time, RMS & Instantaneous Value

[cschear87]

Homework Statement

Given an AC Voltage that varies in time according to the equation:

v(t) = 100 sin(250t)

(i) What is the frequency of this waveform?

(ii) Calculate the time for one complete cycle of the voltage?

(iii) Calculate the instantaneous value of the voltage at time = 6ms.

(iv) Calculate the Root-Mean Square (RMS) value of the AC voltage.

(v) The first time after t=0ms that the instantaneous voltage is 50V.

Homework Equations

v(t) sin (250 x 6 x 10^-3)

The Attempt at a Solution

I'm trying to, obviously, get the third part of this. What I have so far is:
100sin (250pi x 6 x 10^-3)
=100sin (4.71)
In an example in my book it then goes on to multiply 100 x .951... where does the .951 come from and is this what I use for this equation or should I use a different number?
The equation in the book I have is (still 6ms):
v(t) = 100sin (100pi t) V
Their solution is:
100 sin (100pi x 6 x 10^-3)
=100sin (1.88)
=100 x .951
=95.1V
Not sure what I'm missing?

 

[LCKurtz]

It looks like they are using $100\pi$ instead of the $250\pi$. Probably a typo somewhere.

 

[CWatters]

The equation in the book I have is (still 6ms):
v(t) = 100sin (100pi t) V
Their solution is:
100 sin (100pi x 6 x 10^-3)
=100sin (1.88)
=100 x .951
=95.1V

sin(1.8849) = 0.951 if using radians.

In your problem (which is different to the one in the book) you use a different number eg..

= 100sin(4.71)

 

[cschear87]

sin(1.8849) = 0.951 if using radians.

In your problem (which is different to the one in the book) you use a different number eg..

= 100sin(4.71)

OH I see, just got confused. Thank you!