To convert a point from the polar coordinate system to cartesian coordinate system the trigonometric functions sine and cosine are used to solve for the and coordinate of the point. A point in the polar coordinate system is in the form of and a point in the cartesian coordinate system is in the form of . The formulas for the conversion are shown below:

Note, by convention, radians are used to measure angles in polar coordinates.

This example shows how to convert the point in the polar coordinate system to its cartesian coordinate equivalent.

Start by setting up the formula for conversion.

Substitute the radius and angle of the polar coordinates into the formula.

Calculte the result of the multiplication.

Then since we can write the coordinates of the point as:

The cartesian coordinates of the point in polar coordinates are .

This example shows how to convert the point in the polar coordinate system to its cartesian coordinate equivalent.

Start by setting up the formula for conversion.

Substitute the radius and angle of the polar coordinates into the formula.

Calculte the result of the multiplication.

Then since we can write the coordinates of the point as:

The cartesian coordinates of the polar point are .

The formula uses on this page can be derived using the circle definitions of the trigonometric functions sine and cosine and then solving for the anc component of the point.

The Polar Coordinate System describes points in space using an angle and radius relative to the origin.

The Cartesian Coordinate System describes space of one, two, and three dimensions. Each point in space is represented by its distance relative to the origin of the system.

The sine function returns the sine of a number provided in radians. In geometric terms, the function returns the vertical component of the point formed by the angle on the unit circle.

The cosine function returns the cosine of an angle provided in radians. In geometric terms, the function returns the ratio of the right-triangle's adjacent side over its hypotenuse.

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

There are six trigonometric functions that relate to the geometry of the right-triangle sine, cosine, tangent, cosecant, secant, and cotangent. The functions take the angle of a right triangle as input and return a ratio of two of its sides.