# Angles to XY Coordinates

The equations of motion for the first two stages of the trebuchet given in the Equations of Motion section are used to find the angles (Aq, Wq, Sq) of the trebuchet over time. These angles can be used to find the Cartesian coordinates of the different parts of the trebuchet.

Weight CG:

`X = LAs*SIN(Aq) + LW*SIN(Aq+Wq)`

`Y = -LAs*COS(Aq) - LW*COS(Aq+Wq)`

Weight/Arm Point:

`X = LAs*SIN(Aq)`

`Y = -LAs*COS(Aq)`

Arm CG:

`X = -LAcg*SIN(Aq)`

`Y = LAcg*COS(Aq)`

Arm/Sling Point:

`X = -LAl*SIN(Aq)`

`Y = LAl*COS(Aq)`

Projectile:

`X = -LAl*SIN(Aq) - LS*SIN(Aq+Sq)`

`Y = LAl*COS(Aq) + LS*COS(Aq+Sq)`