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: