Key Terms

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 $\frac{\theta }{2\pi }.$ multiplied by the area of the entire circle

cosecant

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

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

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

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

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