[kuh n-tur-muh-nuh s]

  • having a common boundary; bordering; contiguous.
  • meeting at the ends; without an intervening gap: In our calendar system, the close of one year is conterminous with the beginning of the next.
  • coterminous .
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    Also con·ter·mi·nal [kuh n-tur-muh-nl] /kənˈtɜr mə nl/, co·ter·mi·nal [koh-tur-muh-nl] /koʊˈtɜr mə nl/.

    Origin of conterminous

    1625–35; < Latin conterminus having a common border with, equivalent to con- con- + terminus terminus ; see -ous
    Related formscon·ter·mi·nal·ly, con·ter·mi·nous·ly, adverbcon·ter·mi·nal·i·ty, con·ter·mi·nous·ness, nounnon·con·ter·mi·nal, adjectivenon·con·ter·mi·nous, adjectivenon·con·ter·mi·nous·ly, adverb


    [koh-tur-muh-nuh s]
    1. having the same border or covering the same area.
    2. being the same in extent; coextensive in range or scope.
    Also co·ter·mi·nal [koh-tur-muh-nl] /koʊˈtɜr mə nl/.

    Origin of coterminous

    1790–1800; re-formation of conterminous ; see co-
    Related formsco·ter·mi·nous·ly, adverb
    Dictionary.com Unabridged
    Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

    British Dictionary definitions for coterminal


    conterminal (kənˈtɜːmɪnəl) or coterminous (kəʊˈtɜːmɪnəs)

    1. enclosed within a common boundary
    2. meeting at the ends; without a break or interruption
    Derived Formsconterminously, conterminally or coterminously, adverb

    Word Origin for conterminous

    C17: from Latin conterminus, from con- + terminus end, boundary



    1. having a common boundary; bordering; contiguous
    2. coextensive or coincident in range, time, scope, etc
    Collins English Dictionary – Complete & Unabridged 2012 Digital Edition
    © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
    Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

    Word Origin and History for coterminal



    1670s, from Latin conterminus “bordering upon, having a common boundary,” from com- “together, with” (see com- ) + terminus (see terminus ).



    1630s, malformed in English from co- + terminous (see terminal ). Latin purists prefer conterminous .

    Online Etymology Dictionary, © 2010 Douglas Harper

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    Nearby words for coterminal

    1. contention
    2. contentious
    3. contentive
    4. contentment
    5. contents
    6. coterminal
    7. contessa
    8. contest
    9. contestant
    10. contestation
    11. contested

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    About these

    Coterminal angles

    From co -“together”, terminal -“end position”
    Definition: Two angles are coterminal if they are drawn in the standard position
    and both have their
    terminal sides in the same location.
    Try this:
    Adjust the angle below by dragging point A or D multiple times around B, the
    origin , and note when the angles ABC and DBC are coterminal.

    Recall that when an angle is drawn in the
    standard position as above, only the
    terminal sides (BA, BD) varies,
    since the initial side (BC) remains fixed along the positive x-axis.

    If two angles are drawn, they are coterminal if both their
    terminal sides are in the same place – that is, they lie on top of each other.
    In the figure above, drag A or D until this happens.

    If the angles are the same, say both 60°, they are obviously coterminal. But the angles
    can have different measures and still be coterminal. In the figure above, rotate A around counterclockwise
    past 360° until it lies on top of DB. One angle (DBC) has a measure of 72°, and the other (ABC) has a measure of 432°,
    but they are coterminal because their terminal sides are in the same position.
    If you drag AB around twice you find another coterminal angle and so on. There are an infinite number of times you can do this on either angle.

    Either or both angles can be negative

    In the figure above, drag D around the origin counterclockwise so the angle is greater than 360°. Now drag point A around in the opposite direction
    creating a negative angle. Keep going until angle DBC is coterminal with ABC.
    You can see that a negative angle can be coterminal with a positive one.

    How to tell if two angles are coterminal.

    You can sketch the angles and often tell just form looking at them if they are coterminal. Otherwise,
    for each angle do the following:

    • If the angle is positive, keep subtracting 360 from it until the result is between 0 and +360. (In radians, 360° = 2π radians)
    • If the angle is negative, keep adding 360 until the result is between 0 and +360.

    If the result is the same for both angles, they are coterminal.

    Why is this important?

    In trigonometry we use the functions of angles like sin , cos and tan .
    It turns out that angles that are coterminal have the same value for these functions.
    For example, 30&deg, 390° and -330° are coterminal, and so sin30&deg, sin390° and sin(-330°) and all have the same value (0.5).

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    Other trigonometry topics


    • Angle definition, properties of angles
    • Standard position on an angle
    • Initial side of an angle
    • Terminal side of an angle
    • Quadrantal angles
    • Coterminal angles
    • Reference angle

    Trigonometric functions

    • Introduction to the six trig functions
    • Functions of large and negative angles
    • Inverse trig functions
    • SOH CAH TOA memory aid
    • Sine function (sin) in right triangles
    • Inverse sine function (arcsin)
    • Graphing the sine function
    • Sine waves
    • Cosine function (cos) in right triangles
    • Inverse cosine function (arccos)
    • Graphing the cosine function
    • Tangent function (tan) in right triangles
    • Inverse tangent function (arctan)
    • Graphing the tangent function
    • Cotangent function cot (in right triangles)
    • Secant function sec (in right triangles)
    • Cosecant function csc (in right triangles)

    Solving trigonometry problems

    • The general approach
    • Finding slant distance along a slope or ramp
    • Finding the angle of a slope or ramp


    • Derivatives of trigonometric functions
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