I'm having trouble deriving the area of a circle sector formula, 21r2x. Any help?
I've got,
A=21r2cosxsinx and B=4πr2sinx(1−cosx).
The total area of the sector is A + B, and I can see my answer 'works' by letting x tend to zero... I'm just wondering why if I plug in a value of x to my A+B equation, I don't get what I know the answer should be.
I'm having trouble deriving the area of a circle sector formula, 21r2x. Any help?
I've got,
A=21r2cosxsinx and B=4πr2sinx(1−cosx).
The total area of the sector is A + B, and I can see my answer 'works' by letting x tend to zero... I'm just wondering why if I plug in a value of x to my A+B equation, I don't get what I know the answer should be.
Can't you just work out the fraction of a circle's total area the sector has, and then multiply that by the area of a circle?
I could, but I want to know why my way isn't working.
I haven't been set the question.
For starters, A isn't correct. What happens if x > pi/2 ?
(Or rather your formula for A is correct, but it is not a useful area to be trying to work out. Try to find a different triangle to calculate the area of).
Edit: If you want to do this in a different way, might I suggest polar integration. This is a very odd thing to be doing (and B will be a bitch to calculate).
For starters, A isn't correct. What happens if x > pi/2 ?
(Or rather your formula for A is correct, but it is not a useful area to be trying to work out. Try to find a different triangle to calculate the area of).
Edit: If you want to do this in a different way, might I suggest polar integration. This is a very odd thing to be doing (and B will be a bitch to calculate).
I know how to get the formula in other ways. I'd just like to know why my answer doesn't work (for 0 < x < pi/2). If x = pi/3 the area of the sector should be pi/6 r^2, but A + B is something different.