### All Precalculus Resources

## Example Questions

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

Convert from polar form to rectangular form:

**Possible Answers:**

**Correct answer:**

Start by multiplying both sides by .

Keep in mind that

Remember that

So then,

Now, complete the square.

### Example Question #2 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

**Possible Answers:**

**Correct answer:**

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 #3 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

**Possible Answers:**

**Correct answer:**

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 #4 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

**Possible Answers:**

**Correct answer:**

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 #5 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

**Possible Answers:**

**Correct answer:**

Start by taking the tangent.

Recall that

### Example Question #6 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

**Possible Answers:**

**Correct answer:**

Start by taking the tangent.

Recall that

### Example Question #7 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

**Possible Answers:**

**Correct answer:**

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 #8 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

**Possible Answers:**

**Correct answer:**

Recall that and

Multiply both sides by

Recall that and

### Example Question #9 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

**Possible Answers:**

**Correct answer:**

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 #10 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form.

**Possible Answers:**

**Correct answer:**

Recall that

Multiply both sides by to get rid of the fraction.

Recall that .

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