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How do you find a polar equation of the form #r=f(theta)# for the curve represented by the cartesian equation #x = 3#?

Answer 1

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Answer 2

To find the polar equation ( r = f(\theta) ) for the curve represented by the Cartesian equation ( x = 3 ), substitute ( x = r \cos(\theta) ). Thus, ( r \cos(\theta) = 3 ). Solve this equation for ( r ) to obtain ( r = \frac{3}{\cos(\theta)} ). Hence, the polar equation for the curve is ( r = \frac{3}{\cos(\theta)} ).

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Answer from HIX Tutor

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.