Precalculus

# Key Terms

PrecalculusKey Terms
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,$csc t= 1 y ,y≠0 csc t= 1 y ,y≠0$
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,$cot t= x y ,y≠0 cot t= x y ,y≠0$
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$P P$ 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
an angle whose terminal side lies on an axis
the measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle
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,$sec t= 1 x ,x≠0 sec t= 1 x ,x≠0$
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,$tan t= y x ,x≠0 tan t= y x ,x≠0$
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