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Polar differentiation AND integration?!?!?! watch

1. A curve is defined by the polar equation
The tangents to the curve when r=1 meet at a single point.
Find the area of the region that lies inside the triangle formed by the tangents and the y axis, but outside the area bounded by the curve and the y axis.
I got the area as 3-3π/4
Is this correct??
2. (Original post by Ano123)
A curve is defined by the polar equation
The tangents to the curve when r=1 meet at a single point.
Find the area of the region that lies inside the triangle formed by the tangents and the y axis, but outside the area bounded by the curve and the y axis.
I got the area as 3-3π/4
Is this correct??
Zacken
16Characters....
EricPiphany
3. (Original post by Ano123)
A curve is defined by the polar equation
The tangents to the curve when r=1 meet at a single point.
Find the area of the region that lies inside the triangle formed by the tangents and the y axis, but outside the area bounded by the curve and the y axis.
I got the area as 3-3π/4
Is this correct??
I also got this.
4. (Original post by 16Characters....)
I also got this.
It's a nice question don't you think?
5. (Original post by Ano123)
It's a nice question don't you think?
It was a nice question. Tested quite a few different ideas but was not too long and it "flowed", unlike some questions which just force concepts together.

6. got tagged here by teeEm. Finally maths I can actually do :P
7. A vertical line touches the curve at two points. Show that the area enclosed between the line and the curve is equal to .
8. (Original post by EricPiphany)
A vertical line touches the curve at two points. Show that the area enclosed between the line and the curve is equal to .
OMG, I actually managed to do this.

The two values that concern us are: and

The are bounded in the polar curve (using symmetry) is then:

Now draw the lines corresponding to the two arguments and we get a triangle that has area

So the area required is given by:

as required.
9. (Original post by Zacken)
OMG, I actually managed to do this.

The two values that concern us are: and

The are bounded in the polar curve (using symmetry) is then:

Now draw the lines corresponding to the two arguments and we get a triangle that has area

So the area required is given by:

as required.
Very good, and extra credit for latexing it up
10. (Original post by EricPiphany)
Very good, and extra credit for latexing it up
Thanks for this! I learnt quite a bit about polar shiz from doing it.

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