1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Area of a sector from a chord

  1. Mar 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose we have a circle of radius r, and two points A and B on the circle.

    We want to know the area of the sector cut off by A and B as a function of radius r and AB (the length of SEGMENT AB)

    Without calculus or trig.

    2. Relevant equations

    3. The attempt at a solution

    Part of the question included "is this possible" and after trying for a while, I think not.

    Can I get a confirmation either way?

  2. jcsd
  3. Mar 25, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It depends on what is allowed "without calculus or trig", but I would say yes.
  4. Mar 25, 2014 #3
    My issue is that I feel like since the area of the sector involves the center angle - easily a transcendental given some interger AB value, that there isn't a way to get that transcendental without trig.
  5. Mar 25, 2014 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Of course, you can argue that you don't even know the circumference formula without calculus, or even have the concept of "area" for a circle. That's why I say it depends on what's allowed. Also, I see that you are given the segment AB, which I took to mean the arc AB. If you mean the length of the chord, then I would be more inclined to say no.
  6. Mar 25, 2014 #5
    You're right, I should clarify.

    I am allowed to use "high school geometry."

    I know the area of a circle, I know Pythagorean theorem, I know area of a sector (in terms of radius and central angle) and so on.

    But I could not say anything about the central angle with say, arcsin.
  7. Mar 25, 2014 #6
    We were trolled, no solution.
  8. Mar 25, 2014 #7


    User Avatar
    Science Advisor

    Who was "trolled" and by whom? Where did you get this problem? It's relatively simple to solve but does require trigonometry.
  9. Mar 25, 2014 #8
    My professor asked if it could be done, and if so, show how, for homework.

    In class he revealed that it can't. So we were "trolled" in that we spent a lot of time on it because we figured that professors don't usually ask these if it really can't be done.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted