A-level Maths Question( Radians related)

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abdullahAK
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Hey there.
Currently, I'm in chapter 7( Radians) and one of the worked examples is really confusing me.
Its screenshot is in the next post.
Help will be appreciated.
Thanks in advance.
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abdullahAK
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The pic has been attached down below.
Q: The part towards which the red arrow is drawn, it is:

0.5 * r^2 * sin(pi-theta)= Area of triangle AOC.

My question is, sin*pi=0 so it gets deleted. The remaining part is:

0.5 * r^2 * sin(-theta)=Area of Triangle AOC.

But Area cannot be negative.

Can anybody help me with that?

Again any sort of help will be appreciated.
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Interea
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(Original post by abdullahAK)
The pic has been attached down below.
Q: The part towards which the red arrow is drawn, it is:

0.5 * r^2 * sin(pi-theta)= Area of triangle AOC.

My question is, sin*pi=0 so it gets deleted. The remaining part is:

0.5 * r^2 * sin(-theta)=Area of Triangle AOC.

But Area cannot be negative.

Can anybody help me with that?

Again any sort of help will be appreciated.
We don't get rid of the pi because sin(pi)=0, we can't do that as we're doing sin(pi-theta) as opposed to sin(pi)-sin(theta).

Instead they are using equivalent values: sin(theta)=sin(pi-theta), which you can see is true if you look at the graph of sin.

Hence, they have replaced sin(pi-theta) with sin(theta), which is equivalent (and positive for all values of theta between 0 and pi, which is our range for an angle in a triangle). This leaves you with a positive area.
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abdullahAK
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Got it!
I really appreciate your quick and comprehensive response.
Thanks.
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