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Question about polar coordinates

Say we have r( θ ) explicitly defined. We know that x = rcosθ and y = rsinθ. So can we just substitute r into these x and y expressions and then treat them as parametric equations in θ?
Reply 1
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Mathletics
Yes, since all you'd be left with is x(θ\theta) and y(θ\theta)
Reply 2
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gangsta316
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13
So why do we use polar coordinates if this can be done?
Reply 3
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Mathletics
gangsta316
So why do we use polar coordinates if this can be done?


Depends what you are doing. If you want to find thearea bounded by a curve, for example you might prefer to find ∫r2dθ\displaystyle\int r^2 d\theta rather than ∫ydxdθdθ\displaystyle\int y\frac{dx}{d\theta}d\theta.

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