Tangent Line Area

Level pending

On the coordinate axis, for all θ ∈ [ − π , π ] \theta \in [-\pi,\pi] , Francisco draws a line segment between the points ( cos ⁡ θ , 0 ) (\cos{\theta},0) and ( 0 , sin ⁡ θ ) (0,\sin{\theta}) . If the area of the region drawn by the line segments is A, what is ⌊ 100 A ⌋ \lfloor{100A}\rfloor ?


The answer is 117.

Ryan Broder by Ryan Broder , 23, USA

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1 solution

Logan Dymond
Jan 5, 2014

Trivial, area inside an astroid is 3 8 π r 2 \frac{3}{8}\pi r^2

p.s. AH is bad

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Hi Logan! Can you please tell how would you find the equation of astroid? I tried finding the line joining the two points and got x tan ⁡ θ + y = sin ⁡ θ x\tan\theta +y=\sin\theta but I am not sure how to proceed from here.

Many thanks!

Pranav Arora - 7 years, 3 months ago

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