# How do you convert the polar equation #r=3sintheta# into rectangular form?

Multiply the equation by

Simplify

Make appropriate substitutions

Gather all of the terms to the same side

Complete square using the coefficient of

Add

Rewrite

Check out a tutorial on converting an equation from polar to rectangular

Check out a tutorial on completing the square graphically

Check out a tutorial on completing the square analytically

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To convert the polar equation ( r = 3\sin(\theta) ) into rectangular form, you can use the relationships between polar and rectangular coordinates:

[ x = r\cos(\theta) ] [ y = r\sin(\theta) ]

Substitute ( r = 3\sin(\theta) ) into these equations:

[ x = 3\sin(\theta)\cos(\theta) ] [ y = 3\sin^2(\theta) ]

Using the trigonometric identity ( \sin(2\theta) = 2\sin(\theta)\cos(\theta) ), you can rewrite ( x ) in terms of ( \sin(2\theta) ):

[ x = \frac{3}{2}\sin(2\theta) ]

Thus, the rectangular form of the polar equation ( r = 3\sin(\theta) ) is ( x = \frac{3}{2}\sin(2\theta) ) and ( y = 3\sin^2(\theta) ).

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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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