Vectors - Revision history

Conrad: Remove the Rows section (anchor names are documented on Template:Rt)

2026-10-25T21:52:19Z

Remove the Rows section (anchor names are documented on Template:Rt)

Conrad: Row anchors as zero-height blocks above the image, so a row link shows the whole table

2026-10-25T21:41:13Z

Row anchors as zero-height blocks above the image, so a row link shows the whole table

Conrad: Show the official table image instead of a wikitext copy; row anchors now land on the image

2026-10-25T21:39:57Z

Show the official table image instead of a wikitext copy; row anchors now land on the image

Conrad: Physics reference tables (2025 Edition): new reference table page

2026-10-25T20:25:57Z

Physics reference tables (2025 Edition): new reference table page

New page

{{Physreftable
|name=Vectors
|prev=Prefixes for Powers of 10
|next=Motion and Forces
|desc=Vectors from the NYS Physics Reference Tables (2025 Edition): the relationships between a vector and its components, A squared = Ax squared + Ay squared, cos theta = Ax/A, sin theta = Ay/A and tan theta = Ay/Ax, with the component diagram.
}}
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 ''A''x and ''A''y, 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.

<div style="display:flex;flex-wrap:wrap;gap:16px 32px;align-items:flex-start;">
<div style="min-width:0;">
{| class="wikitable" style="text-align:center;"
! Vectors
|- id="components"
| style="padding:8px 16px;" | ''A''2 = ''A''x2 + ''A''y2
|-
| style="padding:8px 16px;" | cos θ = ''A''x''A''
|-
| style="padding:8px 16px;" | sin θ = ''A''y''A''
|-
| style="padding:8px 16px;" | tan θ = ''A''y''A''x
|}
</div>
<div style="min-width:0;">
[[File:Vectors.png|300px|class=img-fluid|alt=Vectors box from the Physics Reference Tables (2025 Edition): the four component relationships and a right-triangle diagram of A, Ax, Ay and the angle theta]]
</div>
</div>

== 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 (''A''x = ''A'' cos θ, ''A''y = ''A'' sin θ) or the angle from the components. θ is measured from the horizontal (the ''A''x 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.''

@@ Line 7: / Line 7: @@
 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 ''A''<sub>x</sub> and ''A''<sub>y</sub>, 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.
-<span id="components"></span>[[File:Vectors.png|340px|class=img-fluid|alt=Vectors from the Physics Reference Tables (2025 Edition)]]
+<div id="components"></div>
 == What the vectors box shows ==

@@ Line 7: / Line 7: @@
 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 ''A''<sub>x</sub> and ''A''<sub>y</sub>, 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.
-<div style="display:flex;flex-wrap:wrap;gap:16px 32px;align-items:flex-start;">
+<span id="components"></span>[[File:Vectors.png|340px|class=img-fluid|alt=Vectors from the Physics Reference Tables (2025 Edition)]]
 == 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 (''A''<sub>x</sub> = ''A'' cos θ, ''A''<sub>y</sub> = ''A'' sin θ) or the angle from the components. θ is measured from the horizontal (the ''A''<sub>x</sub> 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 ==