Trigonometric Graphs (Precalculus)
Sinusoidal Function
A function that describes a continuous cycle. Sine and cosine are examples of sinusoidal functions. y = A sin (Bx - C) + D y = A cos (Bx - C) + D
Periodic Function
A function that returns the same output for different inputs at regular intervals. All trigonometric functions are periodic.
Phase Shift
A horizontal translation (left or right) of the graph of a trigonometric function. x = C/B
Asymptote
A line that a graph approaches, but never crosses. These lines are placed at input values that are undefined for the function.
Mid-line
A vertical translation (up or down) of the graph of a trigonometric function. Horizontal line equidistant from both the crest and the trough of a wave. y = D
Transformation
Changes made to the graph of a function. (Horizontal Shift, Vertical Shift, Dilation, Reflection)
Cosine Function
Function whose input (x) is an angle measure and whose output (y) is the horizontal leg of a right triangle. When plotted, the coordinates form a wave beginning at the crest or trough.
Secant Function
Function whose input (x) is an angle measure and whose output (y) is the ratio 1 over x.
Cosecant Function
Function whose input (x) is an angle measure and whose output (y) is the ratio of 1 over y.
Cotangent Function
Function whose input (x) is an angle measure and whose output (y) is the ratio x over y.
Tangent Function
Function whose input (x) is an angle measure and whose output (y) is the slope of a line.
Sine Function
Function whose input (x) is an angle measure and whose output (y) is the vertical leg of a right triangle. When plotted, the coordinates form a wave beginning at the node.
Undefined
Has no real solution in mathematics. Dividing by zero and taking the square root of negative numbers are two examples.
Period
Horizontal distance it takes a wave to complete one complete cycle. Period = 2π/B
Frequency
How many wavelengths there are over a certain time.
Node
Location where a sinusoidal graph crosses the midline. The locations on a wave where the amplitude is zero
Crest
Maximum output value (y) of a periodic function. Value of midline plus the amplitude.
Amplitude
Maximum vertical distance a wave varies (above or below) from its mid-line. Amplitude is always reported as positive. Amplitude = |A|
Trough
Minimum output value (y) of a periodic function. Value of the midline minus the amplitude.
Reciprocal
One of a pair of numbers whose product is 1. When the numerator and denominator of a fraction are inverted.
Trigonometric Ratio
Ratio that compares two sides of a right triangle for a given angle.
Limit
The output value (y) that a function "approaches" as the input (x) approaches some value from BOTH sides.
One Sided Limit
The output value (y) that a function "approaches" as the input (x) approaches some value from the right OR left side.
Domain
The set of all possible input values (x) for a function.
Range
The set of all possible output values (y) for a function.
x-intercept (zero, solution, root)
The value of the input (x) when the output (y) is zero. Where the graph of a function crosses the x-axis.
y-intercept
The value of the output (y) when the input (x) is zero. Where the graph of a function crosses the y-axis.
Evaluate a Function
To find the value of the output given an input, or visa-versa.