Resolving a force

Resolving replaces one force by components in chosen directions. The components are not extra forces; together they have exactly the same effect as the original force.

To find the component in any chosen positive direction, measure the angle $\phi$ from that positive direction to the force.

If a force makes an angle $\theta$ anticlockwise from the positive horizontal, then $F_x=F\cos\theta$ and $F_y=F\sin\theta$. An angle greater than 90° gives a negative horizontal component automatically.

An axis is a chosen direction in which components are given signs. Horizontal and vertical axes are natural for forces around a point. On an inclined plane, axes parallel and perpendicular to the plane are usually cleaner.

Sometimes a component is known and the original force is unknown. Use the same equation and rearrange it; do not swap sine and cosine.