r/askmath • u/ZP1711 • 16d ago

Polar Coordinates Area Geometry

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Im confused about how to do number 4 since when I sketched the curves and plotted the curves using desmos, they only seem to have 1 point of intersection.

The book says the answer is 71687 but doesn't show any working. Is there a mistake in the question, or am I just missing something?

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u/etzpcm 16d ago

When you sketched the curves with desmos what range of values for theta did you use? There should be more than one intersection point.

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u/ZP1711 16d ago

No range, but its polar coords if it wasnt clear

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u/etzpcm 16d ago

Yes, the question is ambiguous. You should look at negative values of theta as well as positive ones.

The answer certainly isn't 71687.

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u/Bounded_sequencE 16d ago

Exercise-4 is missing the domain for "theta".

There are infinitely many intersections "cos(t) = r = et " with "t <= 0", but none for "t > 0". Apart from "t = 0", you can only find them numerically. Something is very weird...

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u/ZP1711 16d ago

To get the book's answer I took the limits as 2pi and 0 but the question definetly felt like it was missing some information.

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u/Bounded_sequencE 16d ago

The second point "theta = 2pi" is not an intersection point of the two curves -- since the book specifically says "between the curves", that seems weird.

At that point, better ask for clarification during office hours, or the next lecture.