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Mathematics LibreTexts

5.6.1: Key Terms

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    116119
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    Key Terms

    adjacent side
    in a right triangle, the side between a given angle and the right angle
    angle
    the union of two rays having a common endpoint
    angle of depression
    the angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned lower than the observer
    angle of elevation
    the angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned higher than the observer
    angular speed
    the angle through which a rotating object travels in a unit of time
    arc length
    the length of the curve formed by an arc
    area of a sector
    area of a portion of a circle bordered by two radii and the intercepted arc; the fraction θ 2π θ 2π multiplied by the area of the entire circle
    cosecant
    the reciprocal of the sine function: on the unit circle, csct= 1 y ,y0 csct= 1 y ,y0
    cosine function
    the x-value of the point on a unit circle corresponding to a given angle
    cotangent
    the reciprocal of the tangent function: on the unit circle, cott= x y ,y0 cott= x y ,y0
    coterminal angles
    description of positive and negative angles in standard position sharing the same terminal side
    degree
    a unit of measure describing the size of an angle as one-360th of a full revolution of a circle
    hypotenuse
    the side of a right triangle opposite the right angle
    identities
    statements that are true for all values of the input on which they are defined
    initial side
    the side of an angle from which rotation begins
    linear speed
    the distance along a straight path a rotating object travels in a unit of time; determined by the arc length
    measure of an angle
    the amount of rotation from the initial side to the terminal side
    negative angle
    description of an angle measured clockwise from the positive x-axis
    opposite side
    in a right triangle, the side most distant from a given angle
    period
    the smallest interval P P of a repeating function f f such that f(x+P)=f(x) f(x+P)=f(x)
    positive angle
    description of an angle measured counterclockwise from the positive x-axis
    Pythagorean Identity
    a corollary of the Pythagorean Theorem stating that the square of the cosine of a given angle plus the square of the sine of that angle equals 1
    quadrantal angle
    an angle whose terminal side lies on an axis
    radian
    the measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle
    radian measure
    the ratio of the arc length formed by an angle divided by the radius of the circle
    ray
    one point on a line and all points extending in one direction from that point; one side of an angle
    reference angle
    the measure of the acute angle formed by the terminal side of the angle and the horizontal axis
    secant
    the reciprocal of the cosine function: on the unit circle, sect= 1 x ,x0 sect= 1 x ,x0
    sine function
    the y-value of the point on a unit circle corresponding to a given angle
    standard position
    the position of an angle having the vertex at the origin and the initial side along the positive x-axis
    tangent
    the quotient of the sine and cosine: on the unit circle, tant= y x ,x0 tant= y x ,x0
    terminal side
    the side of an angle at which rotation ends
    unit circle
    a circle with a center at (0,0) (0,0) and radius 1.
    vertex
    the common endpoint of two rays that form an angle

    5.6.1: Key Terms is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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