### All Precalculus Resources

## Example Questions

### Example Question #31 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation into polar form.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute these values into the equation.

Now, manipulate the equation so that the terms with are on the same side.

Factor out the .

Divide both sides by .

### Example Question #32 : Convert Polar Equations To Rectangular Form And Vice Versa

Conver the rectanglar equation into polar form.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute these values into the equation.

Now, manipulate the equation so that the terms with are on the same side.

Factor out the .

Divide both sides by .

### Example Question #33 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute these values into the equation.

Now, manipulate the equation so that the terms with are on the same side.

Factor out the .

Divide both sides by .

### Example Question #34 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute these values into the equation.

Now, manipulate the equation so that the terms with are on the same side.

Factor out the .

Divide both sides by .

### Example Question #35 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert from rectangular form to polar.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute those into the equation.

Expand the equation.

Add to both sides.

Factor out .

Remember that .

Divide both sides by .

### Example Question #36 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute those into the equation.

Expand this equation.

Add to both sides.

Factor out on the left side of the equation.

Recall that

Divide both sides by .

### Example Question #37 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation into polar form.

**Possible Answers:**

**Correct answer:**

Recall that and .

Substitute those into the equation.

Expand this equation.

Subtract both sides by .

Factor out the .

At this point, either or . Let's continue solving the latter equation to get a more meaningful answer.

Add to both sides.

Divide both sides by to solve for .

Recall that and that .

### Example Question #38 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form:

**Possible Answers:**

**Correct answer:**

Recall that

Substitute that into the equation.

Recall that,

### Example Question #39 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation to polar form:

**Possible Answers:**

**Correct answer:**

Recall that .

Substitute that into the equation.

Now, isolate the on one side.

Recall that,

### Example Question #40 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the rectangular equation into polar form.

**Possible Answers:**

**Correct answer:**

Recall that

Substitute that into the equation.

Recall that,

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