# Precalculus : Polar Coordinates

## Example Questions

### Example Question #50 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert to polar form

Explanation:

Re-arrange the left side so that is next to , and factor the 4 out on the right side :

Make the substitutions and :

take the square root of both sides

divide both sides by r

subtract from both sides

### Example Question #121 : Polar Coordinates And Complex Numbers

Write the equation in polar form

Explanation:

First re-arrange the original equation so that the 4 is factored out on the right side, and put and next to each other:

Make the substitutions and :

take the square root of both sides

divide both sides by r

### Example Question #122 : Polar Coordinates And Complex Numbers

Which is equivalent to ?

Explanation:

To convert, substitute and :

divide both sides by r

multiply both sides by 2

divide both sides by cosine squared

### Example Question #123 : Polar Coordinates And Complex Numbers

Convert to polar form:

Explanation:

Convert by making the substitutions and :

subtract from both sides

factor out r

divide

### Example Question #124 : Polar Coordinates And Complex Numbers

Convert the polar coordinates  to rectangular form.

Explanation:

We begin by recalling that polar coordinates are expressed in the form , where  is the radius (the distance from the origin to the point) and  is the angle formed between the postive x-axis and the radius.

We can find our x-coordinate and y-coordinate in rectangular form quite easily by keeping in mind two equations.

or

or

Substituting in both of these gives respectively

Therefore, the rectangular coordinates of our point are

### Example Question #125 : Polar Coordinates And Complex Numbers

Convert the polar coordinates to rectangular coordinates:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question,

The rectangular coordinates are

### Example Question #126 : Polar Coordinates And Complex Numbers

Convert the polar coordinates to rectangular coordinates:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question,

The rectangular coordinates are

### Example Question #127 : Polar Coordinates And Complex Numbers

Convert the polar coordinates to rectangular coordinates:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question,

The rectangular coordinates are

### Example Question #128 : Polar Coordinates And Complex Numbers

Convert the polar coordinates to rectangular coordinates:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question,

The rectangular coordinates are

### Example Question #129 : Polar Coordinates And Complex Numbers

Convert the polar coordinates to rectangular coordinates:

Explanation:

To convert polar coordinates  to rectangular coordinates ,

Using the information given in the question,

The rectangular coordinates are