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.
