Vectors · Physics Reference Tables (2025 Edition)
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The Vectors box from the Reference Tables for Physical Science: Physics (2025 Edition) gives the four relationships between a vector A, its horizontal and vertical components Ax and Ay, and the angle θ it makes with the horizontal, with a diagram of the right triangle they form. It supports HS-PS2-1 (forces and velocities at an angle) and any question in which a force, velocity or displacement has to be split into components or rebuilt from them.
| Vectors |
|---|
| A2 = Ax2 + Ay2 |
| cos θ = AxA |
| sin θ = AyA |
| tan θ = AyAx |
What the vectors box shows
The first relationship is the Pythagorean theorem for the magnitude of a vector from its perpendicular components; the other three come from the right triangle in the diagram and give the components from the magnitude and angle (Ax = A cos θ, Ay = A sin θ) or the angle from the components. θ is measured from the horizontal (the Ax side). The 2006 edition of the physics reference tables had a fuller Geometry and Trigonometry table (areas, volumes and the trigonometric ratios); the 2025 edition keeps only these vector relationships.
Regents Exam Questions
Released Regents questions that cannot be answered without this table, listed by exam. Each link opens the question with its answer key; the standard is the one the question assesses.
No released question has needed this table yet.