Help with a question (1 Viewer)

calamebe · Sep 6, 2015

Hey, I was doing a James Ruse past paper and there's this one question I couldn't do, any help would be appreciated, thanks!
http://m.imgur.com/USXsS4N

Drsoccerball · Sep 6, 2015

calamebe said:
Hey, I was doing a James Ruse past paper and there's this one question I couldn't do, any help would be appreciated, thanks!
http://m.imgur.com/USXsS4N

It is given that the area of the major segment is 2 times the minor segment:
$$ Minor segment area: $ \frac{r^2}{2}(\theta -sin\theta)$

$$ Major segment area: $ r^2(\theta -sin\theta)$

$$ Area of circle = Major area +minor area $ \pi =\frac{3\theta}{2} -\frac{3sin\theta}{2}$

$3sin\theta = 3\theta -2\pi$

calamebe · Sep 6, 2015

Drsoccerball said:
It is given that the area of the major segment is 2 times the minor segment:
$$ Minor segment area: $ \frac{r^2}{2}(\theta -sin\theta)$

$$ Major segment area: $ r^2(\theta -sin\theta)$

$$ Area of circle = Major area +minor area $ \pi =\frac{3\theta}{2} -\frac{3sin\theta}{2}$

$3sin\theta = 3\theta -2\pi$

Where does the θ-sinθ come from, my teacher never taught us that. What is the rule/theorem/thingy called so I can teach myself?

Drsoccerball · Sep 6, 2015

calamebe said:
Where does the θ-sinθ come from, my teacher never taught us that. What is the rule/theorem/thingy called so I can teach myself?

Its the area of a segment... It can be derived by the area of the whole sector $\frac{\theta r^2}{2}$ and subtract it from $\frac{r^2 sin\theta}{2}$

Help with a question (1 Viewer)

calamebe

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Drsoccerball

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calamebe

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Drsoccerball

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