# Precalculus : Convert Rectangular Equations To Polar Form

## Example Questions

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

Convert  to polar coordinates.

Explanation:

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.

Explanation:

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:

Explanation:

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.

Explanation:

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.

Explanation:

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 #6 : Convert Rectangular Equations To Polar Form

Convert the rectangular equation to polar form.

Explanation:

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 #7 : Convert Rectangular Equations To Polar Form

Convert the rectangular equation to polar form.

Explanation:

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 #8 : Convert Rectangular Equations To Polar Form

Convert from rectangular form to polar.

Explanation:

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 #9 : Convert Rectangular Equations To Polar Form

Convert the rectangular equation to polar form.

Explanation:

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 #10 : Convert Rectangular Equations To Polar Form

Convert the rectangular equation into polar form.

Explanation:

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 .

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