Applications of Radian Measure

Key Questions

  • What are some applications of using radian measure?

    In physics you use radians to describe circular motion, in particular you use them to determine angular velocity, omega.
    You may be familiar with the concept of linear velocity given by the ratio of displacement over time, as:
    v=(x_f-x_i)/t
    where x_f is the final position and x_i is the initial position (along a line).
    Now, if you have a circular motion you use the final and initial ANGLES described during the motion to calculate velocity, as:
    omega=(theta_f-theta_i)/t
    Where theta is the angle in radians.
    omega is angular velocity measured in rad/sec.
    enter image source here
    (Picture source: http://francesa.phy.cmich.edu/people/andy/physics110/book/chapters/chapter6.htm)

    Have a look to other rotational quantities you'll find a lot of ...radians!

    Gió · 1 · Jan 11 2015
  • How do you calculate the length of an arc and the area of a sector?

    For any theta, the length of the arc is given by the formula (if you work in radians, which you should:
    ![mathwarehouse.com](useruploads.socratic.org)
    The area of the sector is given by the formula (theta r^2)/2

    Why is this?
    If you remember, the formula for the perimeter of a circle is 2pir.
    In radians, a full circle is 2pi. So if the angle theta = 2pi, than the length of the arc (perimeter) = 2pir. If we now replace 2pi by theta, we get the formula S = rtheta

    If you remember, the formula for the area of a circle is pir^2.
    If the angle theta = 2pi, than the length of the sector is equal to the area of a circle = pir^2. We've said that theta = 2pi, so that means that pi = theta/2.
    If we now replace pi by theta/2, we get the formula for the area of a sector: theta/2r^2

    Nico Ekkart · 5 · Dec 19 2014
  • How do you approximate the length of a chord given the central angle and radius?

    Let's call the cord AB and the centre of the circle C

    Then if you divide the cord in half at M you get two equal, but mirrored triangles Delta CMA and Delta CMB. These are both rectangular at M. (You should draw this yourself right now !).

    angle ACM is half the central angle that was given
    (and angleBCMis the other half)

    Then sin angle ACM=(AM)/(AC) ->AM=AC*sin angle ACM

    Since you know the radius (AC) and the central angle (remember angleACM=half of that), you just plug in these values to get an accurate result for half the chord (so don't forget to double it for your final answer)

    MeneerNask · 1 · Jan 13 2015
  • What are some example problems involving angular speed?

    Answer:

    See examples in explanation

    Explanation:

    Earth's day/night spin about it axis is with

    angular speed = 2pi radian / 24-hour day.

    Earths revolution about Sun is owith

    angular speed = #2pi) radian / 365.26-day year.

    Rotors making electro-mechanical rotations have high angular

    speeds of

    kKpi radian / minute, k > 1,

    making thousands of rpm ( revolutions / minute ).
    ,

    A. S. Adikesavan · 1 · Aug 10 2018

Questions

Graphing Trigonometric Functions