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C2 Urgent Help Please...

Hi all,
I have a serious issue with sectors/arcs/segments in C2. In class I was taught to use the formula 0.5r^2(0-sin0) to calculate the area of a segment. Incidentally, 0 represents theta.
However, this is now the second exam question I've encountered where the formula is used in the reverse order. So they use 0.5r^2(sin0-0) and I do no understand why.
For the question in the image below, I did 0.5(9)(1.0766-sin(1.0766)) = 8.806 for the area.
The mark scheme reads: 0.5(9)(sin(1.0766)-0.5(9)(1.0766) = 3.507 for the area i.e the calculation is in reverse order.
I would appreciate it if someone could enlighten me.
Thanks in advance.
(edited 6 years ago)
Posted from TSR Mobile
That's not a segment. In this question the sector is inside the triangle rather that the other way around.

Might be an idea not to think in terms of formulae. Try instead to understand the specific problem.
Reply 2
Original post by Wolfram Alpha
Hi all,
I have a serious issue with sectors/arcs/segements in C2. In class I was taught to use the formula 0.5r^2(0-sin0) to calculate the area of a segment. Incidentally, 0 represents theta.
However, this is now the second exam question I've encountered where the formula is used in the reverse order. So they use 0.5r^2(sin0-0) and I do no understand why.
For the question in the image below, I did0.5(9)(1.0766-sin(1.0766) = 8.806 for the area.
The mark scheme reads: 0.5(9)(sin(1.0766)-0.5(9)(1.0766).
I would appreciate it if someone could enlighten me.
Thanks in advance.

Memorising more formulas that you need is a bad idea, especially if you don't understand where the formula comes from. You'll end up blindingly following a formula for a question that shouldn't need it, which you've done here.

The only area formula that you need to know is the area of a sector:

A=12r2θA=\frac{1}{2}r^2\theta

If you look at the shaded area in the diagram you'll see that it's not a segment but can be found by subtracting the area of a sector from the area of a triangle. Can you see this?

Ignore the mark scheme and try finding this area using this method and post your working if you get stuck.
Original post by Wolfram Alpha
Hi all,
I have a serious issue with sectors/arcs/segments in C2. In class I was taught to use the formula 0.5r^2(0-sin0) to calculate the area of a segment. Incidentally, 0 represents theta.
However, this is now the second exam question I've encountered where the formula is used in the reverse order. So they use 0.5r^2(sin0-0) and I do no understand why.
For the question in the image below, I did 0.5(9)(1.0766-sin(1.0766)) = 8.806 for the area.
The mark scheme reads: 0.5(9)(sin(1.0766)-0.5(9)(1.0766) = 3.507 for the area i.e the calculation is in reverse order.
I would appreciate it if someone could enlighten me.
Thanks in advance.


Okay, so you'd find the area of the original triangle by doing; (1/2)x(b)x(h)
Then you'd find the area of the Sector by using the formula; (1/2)x(r^2)x(θ)

Do; [Area of Triangle] - [Area of Sector] to get your shaded region

You wouldn't use the rule for Area of segment (1/2)x(r^2)x(θ-sinθ) as this is a sector.

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