# How do you graph #r^2=3sin2θ#?

Please see below.

We can use this to convert equation in polar coordinates to an equation with Cartesian coordinates.

Note that

The function appears as follows. graph{((x^2+y^2)^2-6xy)(x-y)=0 [-5, 5, -2.5, 2.5]}

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To graph the polar equation ( r^2 = 3 \sin(2\theta) ), follow these steps:

- Rewrite the equation in terms of ( r ) and ( \theta ) separately.
- Plot points for various values of ( \theta ), calculate the corresponding values of ( r ), and plot them on the polar coordinate system.
- Connect the plotted points to form the graph.

Since ( r^2 = 3 \sin(2\theta) ), we can rewrite it as ( r = \sqrt{3 \sin(2\theta)} ).

Now, for various values of ( \theta ), calculate ( r ) using the equation ( r = \sqrt{3 \sin(2\theta)} ). Plot these points on the polar coordinate system. Ensure that ( \theta ) varies from ( 0 ) to ( 2\pi ) to cover one complete cycle of the graph.

After plotting a sufficient number of points, connect them to form the graph of the polar equation ( r = \sqrt{3 \sin(2\theta)} ). This graph represents the polar curve corresponding to the given equation.

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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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