### All Precalculus Resources

## Example Questions

### Example Question #1 : Convert Rectangular Equations To Polar Form

Convert to polar coordinates.

**Possible Answers:**

**Correct answer:**

Write the Cartesian to polar conversion formulas.

Substitute the coordinate point to the equations and solve for .

Since is located in between the first and second quadrant, this is the correct angle.

Therefore, the answer is .

### Example Question #2 : Convert Rectangular Equations To Polar Form

Convert to polar form.

**Possible Answers:**

**Correct answer:**

Write the Cartesian to polar conversion formulas.

Substitute the coordinate point to the equations to find .

Since is not located in between the first quadrant, this is not the correct angle. The correct location of this coordinate is in the third quadrant. Add radians to get the correct angle.

Therefore, the answer is .

### Example Question #3 : Convert Rectangular Equations To Polar Form

Convert the rectangular equation to polar form:

**Possible Answers:**

**Correct answer:**

Because and , substitute those values in the rectangular form.

Now, expand the equation.

Subtract from both sides.

Recall the trigonometric identity

Factor the equation.

### Example Question #4 : Convert Rectangular Equations To Polar Form

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 #5 : Convert Rectangular Equations To Polar Form

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 #61 : Polar Coordinates And Complex Numbers

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 #62 : Polar Coordinates And Complex Numbers

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 #63 : Polar Coordinates And Complex Numbers

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 #64 : Polar Coordinates And Complex Numbers

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 #65 : Polar Coordinates And Complex Numbers

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 .