# How do you find the length of cardioid #r = 1 - cos theta#?

8

arc length in polar is

here

so

So, assuming length is of one full revolution.....

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To find the length of the cardioid ( r = 1 - \cos(\theta) ), you can use the formula for arc length in polar coordinates:

[ L = \int_{\alpha}^{\beta} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} , d\theta ]

where ( \alpha ) and ( \beta ) are the limits of integration that cover the desired portion of the curve.

For the cardioid ( r = 1 - \cos(\theta) ), you need to find ( \frac{dr}{d\theta} ) and then integrate using the appropriate limits.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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