Physics

Vectors can be broken down into horizontal and vertical pieces using basic trigonometry. When a vector points at angle $\theta$ from the $x$-axis, imagine dropping perpendiculars to each axis—the cosine gives you the $x$-component and the sine gives you the $y$-component, each scaled by the vector's magnitude. This decomposition is fundamental because it lets you work with vectors algebraically instead of geometrically.

Vectors can be broken down into horizontal and vertical pieces using basic trigonometry. When a vector points at angle $\theta$ from the $x$-axis, imagine dropping perpendiculars to each axis—the cosine gives you the $x$-component and the sine gives you the $y$-component, each scaled by the vector's magnitude. This decomposition is fundamental because it lets you work with vectors algebraically instead of geometrically.