1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Radians v. Degrees

  1. Mar 7, 2014 #1
    1. The problem statement, all variables and given/known data

    The voltage across a 60μF capacitor is described by the equation vC =(18 V) cos(200t), where t is in seconds.

    What is the voltage across the capacitor at t =0.010 s?

    2. Relevant equations


    3. The attempt at a solution

    When you use degrees the answer is 18V and when you use radians its -7.5 V (the correct answer). Can someone explain why you must use radians here? It's been a while since using these in math class so the simpler explanation the better if you wouldn't mind :) (maybe I am missing something obvious).

  2. jcsd
  3. Mar 7, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    For your formula, you should be using radians rather than degrees. The argument of the cosine is going to be a pure number without units, which suggests that radian measure is the one to use.
  4. Mar 7, 2014 #3
    Why would using degrees not give a unitless number?
  5. Mar 7, 2014 #4
    You should be using radians because you are dealing with AC. This is obvious because the voltage is given as a cosine wave and alternating current is a waveform (whereas DC is approximated by a "linear" voltage). The AC has an angular frequency of 200 radians because the general equation for a cosine wave is Acos(kx+ωt).
  6. Mar 7, 2014 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Technically, a degree of angular measure is not strictly dimensionless; it represents part of the arc of a circle, but it cannot be decomposed into basic units of mass, length, or time. The radian, by definition, is the ratio of the length of a circular arc to the radius of the arc, and as such, is dimensionless (L/L).

  7. Mar 7, 2014 #6
    I have a different perspective. There is nothing fundamentally wrong with using degrees per second rather than radians per second. However, in physics, it is customary to work in terms of radians per second. Maybe that's because, if you wanted to calculate the rate of change of V with respect to time, you would have a real problem if you were working in terms of degrees/sec.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted