Home > Calculus > Determining the Length of a Polar Curve

Sketch the curve with the given polar equation...?

I recognize it as a rose curve, but I don't know how to do it the way the question's asking.

Answer 1

(see explanation)

...does anyone know how to format a table in Socratic LaTeX?

The period of #2+\sin\color(red)(3)\theta# is #2\pi\div\color(red)(3)=(2\pi)/3#. At #\pi/6n# the graph reaches its highest points, the amplitude of 2 (which is 3 due to the graph being shifted upwards).

From a table of #\theta# with intervals of #\pi/6#, calculating #r#:

Cartesian
Polar

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Answer 2

Christopher Agresta

To sketch the curve with the given polar equation, follow these steps:

Analyze the form of the polar equation to determine the shape of the curve.
Plot points on the curve by substituting various values of θ into the equation.
Use these points to sketch the curve, paying attention to symmetry, asymptotes, and any other notable features based on the equation.
Label any key points or features on the curve to provide additional context.

If you provide the specific polar equation, I can guide you through these steps to sketch the curve accurately.

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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.