# Precalculus : Convert Polar Equations To Rectangular Form and vice versa

## Example Questions

### Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert from polar form to rectangular form:

Explanation:

Start by multiplying both sides by .

Keep in mind that

Remember that

So then,

Now, complete the square.

### Example Question #3 : Polar Coordinates

Convert the polar equation to rectangular form:

Explanation:

Start by multiplying both sides by .

Remember that

Keep in mind that

So then,

Now, complete the square.

This is a graph of a circle with a radius of  and a center at

### Example Question #4 : Polar Coordinates

Convert the polar equation into rectangular form:

Explanation:

Remember that

So then  becomes

Now, multiply both sides by  to get rid of the fraction.

Since  the rectangular form of this equation is

### Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

Explanation:

Start by using the double angle formula for .

Substitute that into the equation gives the following:

Because we need  and  to get  and  respectively, multiply both sides by .

Now, recall that .

### Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

Explanation:

Start by taking the tangent.

Recall that

### Example Question #7 : Polar Coordinates

Convert the polar equation to rectangular form:

Explanation:

Start by taking the tangent.

Recall that

### Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

Explanation:

Recall that

Substituting this into the given equation gives

Multiply both sides by  to get rid of the fraction.

Recall that  and that

### Example Question #9 : Polar Coordinates

Convert the polar equation into rectangular form:

Explanation:

Recall that  and

Multiply both sides by

Recall that  and

### Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

Explanation:

Recall that

Plugging this into the equation gives us

Multiply both sides by  to get rid of the fraction.

Recall that

So then the rectangular form of the equation is

### Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form.