# JavaScript Arithmetic (Math) Sin & Cos to create a vector given direction & distance

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## Example

If you have a vector in polar form (direction & distance) you will want to convert it to a cartesian vector with a x and y component. For referance the screen coordinate system has directions as 0 deg points from left to right, 90 (PI/2) point down the screen, and so on in a clock wise direction.

``````var dir = 1.4536; // direction in radians
var dist = 200; // distance
var vec = {};
vec.x = Math.cos(dir) * dist; // get the x component
vec.y = Math.sin(dir) * dist; // get the y component
``````

You can also ignore the distance to create a normalised (1 unit long) vector in the direction of `dir`

``````var dir = 1.4536; // direction in radians
var vec = {};
vec.x = Math.cos(dir); // get the x component
vec.y = Math.sin(dir); // get the y component
``````

If your coordinate system has y as up then you need to switch cos and sin. In this case a positive direction is in a counterclockwise direction from the x axis.

``````// get the directional vector where y points up
var dir = 1.4536; // direction in radians
var vec = {};
vec.x = Math.sin(dir); // get the x component
vec.y = Math.cos(dir); // get the y component
``````

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