Representations of Trigonometric Functions

Absolute Value Function

a function that contains an algebraic expression within absolute value symbols

Trigonometric Function

a function whose rule is given by a trigonometric ratio (Sin, Cosine, Tangent, or inverses)

Asymptote

a line that a graph approaches but never intersects

Sinosoidal

a mathematical curve that describes a smooth repetitive oscillation. A sine wave is a continuous wave.

standard Position

an angle drawn on the x-y plane with its vertex at the origin and its initial side along the positive x-axis.

Quadrantal Angle

an angle that terminates on an axis

Coterminal

angles that have the same initial and terminal sides

Period

the distance required for the function to complete one full cycle.

Terminal Side

the ending position of the ray when creating an angle

Minimum

the point on a curve where the slope changes from Negative to positive; where y is the least of all y values; The lowest point of a parabola.

Maximum point

the point on a curve where the slope changes from positive to negative; where y is the largest of all y values; The highest point of a parabola.

Radian

57.3 degrees; A unit of angle measure based on arc length; 1/2 pi of the revolution abbreviated "rad"

Odd Function

A function that is symmetric with respect to the origin; -f(x) = f(-x) rotation 180º

Even Function

A function that is symmetric with respect to the y-axis; f(x)=f(-x)

Phase Shift

A horizontal translation of a periodic function

Vertical Translation

A shift in which a plane figure moves vertically. f(x)+k Moves the graph up or down; The y-coordinate changes

Zeroes

An x-value that makes f(x) equal 0; x-intercepts

quadrantal

Lying on an axis

Inverse

Opposite in position, direction, order or effect.

Initial Side

The fixed ray of an angle in standard position along the positive x-axis.

Extrema

The maximum and minimum values of a function.

Cotangent

The reciprocal of Tangent adjacent/opposite x/y

Secant

The reciprocal of the Cosine function of an acute angle of a right triangle; hypotenuse/adjacent r/x a line that intersects a circle at two points;

Cosecant

The reciprocal of the Sine function of an acute angle of a right triangle; hypotenuse/opposite csc r/y

Midline

The resting position of the wave; Divides body into bottom and upper halves;

One to One Function

each element of the domain pairs to exactly one unique element of the range; A function that has one unique output (y value) for every unique input (x value)

Unit Circle

has a radius of 1 unit and its center is the origin of the coordinate plane; (cos, sin)

Symmetry

having the same shape, size, and position on both sides of a dividing line

Increasing

interval when the y-value gets bigger as the x-value increases

Decreasing

interval when the y-values are getting smaller as the x values increase

Intercepts

points where a line crosses the x-axis and y-axis

Cyclical

repeating, recurring in a pattern; Occurring in cycles

Positive Angle

rotate terminal side counter clockwise

Negative Angle

rotation of the terminal side is clockwise

Oscillation

the act or state of swinging back and forth with a steady, uninterrupted rhythm

Amplitude

the height from the mean, or rest, value of the function to its maximum or minimum

Frequency

the number of complete wavelengths that pass a point in a given time

Quadratic Function

A function in which the greatest power of the variable is 2.

Rational Function

A function that can be written as a polynomial divided by a polynomial.

Trigonometric Ratios

Sine, Cosine, and Tangent; Ratio that describes a relationship between a side and an angle of a triangle

End Behavior

The behavior of the graph of f(x) as x approaches positive infinity or negative infinity; Describes how the values of a function behave at each end of the graph.

Domain

The set of input values of a function.

Range

The set of output values of a function.

Reference Angle

The smallest angle that the terminal side of a given angle makes with the x-axis. Angle between the terminal side and the x-axis.

Continuity

Uninterrupted connection in space, time, operation, or development.

Discontinuity

a distinct break in physical continuity or sequence in time; a point at which a function is discontinuous or undefined.