# Precalculus : Polar Coordinates

## Example Questions

### Example Question #30 : Convert Polar Equations To Rectangular Form And Vice Versa

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

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

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

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

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

Convert from rectangular form to polar.

Explanation:

Recall that  and .

Substitute those into the equation.

Expand the equation.

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.

Explanation:

Recall that  and .

Substitute those into the equation.

Expand this equation.

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.

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.

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:

Explanation:

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: