A mathematically oriented candy company is putting their valentines day candy into boxes in the shape of a cardioid. In polar coordinates, the equation of the cardioid is:
r=1−sin(Θ)
If the company puts the candy box into a rectangular shipping box as shown below, What are the dimensions of the shipping box?

Question

A mathematically oriented candy company is putting their valentines day candy into boxes in the shape of a cardioid. In polar coordinates, the equation of the cardioid is:
r=1−sin(Θ)
If the company puts the candy box into a rectangular shipping box as shown below, What are the dimensions of the shipping box?

directrix · Answer

> candy box into a rectangular shipping box as shown below, 

Is there a diagram that is needed?

rmrjr22 · Answer

attachment

directrix · Answer

Take a look at the graph of the cardioid. http://www.wolframalpha.com/input/?i=+r%3D+1+%E2%88%92+sin%28theta%29

rmrjr22 · Answer

ok... I already have one graphed from 0 to 2Pi
I do not know how to find the max area from x and y.

directrix · Answer

I was thinking that we need what might be thought of as the "length" and "width" of the cardioid. I cannot think of a way to get those at the moment. Another thought - how do we know the height of the cardioid when it is a plane figure? And, headed for a 3-d box.

rmrjr22 · Answer

Finding the derivative which is the slope of the line at the curve...
I gather if theta is 30 degrees, that is the highest point and lowest is -2 on the graph. I am not sure how to find the height of 30 degrees which lies on 0.50 horizonately, but do not know how to find the y value above the origin or 0 mark

hartnn · Answer

its not 0.5 horizontally, its 0.5 radially (because u got r = 0.5, right ?)
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can you find 'x' and 'y' from that 30-60-90 triangle ?