cos
Summary
Cosine (cos) is the trigonometric ratio adjacent/hypotenuse. In physics it gives a vector's component along the axis the angle is measured from, such as Fx = F cos θ. Most testable: cos is 1 at 0° and 0 at 90°, so that component shrinks as the angle grows.
Detail
Meaning: Cosine is a trigonometric ratio: for an angle in a right triangle, the adjacent side divided by the hypotenuse. In physics it gives the part of a vector that lies along the axis the angle is measured from. Values to memorize: cos 0° = 1, cos 30° ≈ 0.87, cos 45° ≈ 0.71, cos 60° = 0.5, cos 90° = 0.
Equation: cos θ = adjacent/hypotenuse, so Fx = F cos θ. F is the force magnitude (N), θ is the angle from the x-axis (degrees or radians), and Fx is the x-component (N). Cosine itself has no units. For work, W = Fd cos θ, where W is in J, d is displacement in m, and θ is the angle between force and displacement.
On the MCAT: A projectile launched at angle θ has horizontal velocity v cos θ. A block on an incline feels a weight component mg cos θ perpendicular to the surface. An angled pull does work Fd cos θ. Questions ask how a quantity changes as θ increases, often using the 30°, 45° and 60° values without a calculator.
Common confusion: Using cos when the angle is measured from the other axis. Cos goes with the side that touches the angle. On an incline of angle θ, the component of weight parallel to the surface is mg sin θ and the perpendicular one is mg cos θ. Draw the triangle before choosing.
Sources
- Physics (Giancoli)
- University Physics (Young and Freedman)
- Fundamentals of Physics (Halliday, Resnick, Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.