5.6.1: Key Terms

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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 $\frac{θ}{2 π}$ multiplied by the area of the entire circle

cosecant: the reciprocal of the sine function: on the unit circle, $\csc t = \frac{1}{y}, y \neq 0$

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, $\cot t = \frac{x}{y}, y \neq 0$

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 $P$ of a repeating function $f$ such that $f (x + P) = f (x)$

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, $\sec t = \frac{1}{x}, x \neq 0$

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, $\tan t = \frac{y}{x}, x \neq 0$

terminal side: the side of an angle at which rotation ends

unit circle: a circle with a center at $(0, 0)$ and radius 1.

vertex: the common endpoint of two rays that form an angle

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