Level 445 Level 447
Level 446

Graphs of Trigonometric Functions


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Amplitude
The height (crest) or depth (trough) of a wave measured from the midline. It's value is half of the range.
Asymptote
An imaginary line on a graph that acts as a boundary line.
Crest
Highest point of a wave. (maximum y-value)
Domain
The ______________________ is all the possible INPUT, X, values.
Intercepts
The point(s) at which the graph intersects or touches the x-axis or y-axis.
Periodic Functions
Functions that repeat their values over a regular interval.
Period or Wavelength
The distance required for a function to complete one full cycle. The Greek letter λ (lambda) is used to represent wavelength. (Period = 2π/b)
Range
The difference between the greatest number and the least number in a set of data.
Transformation
a movement on the cartesian plane
Trough
Lowest point of a wave. (minimum y-value)
Undefined
when dividing a nonzero number by zero,
La Buena Onda
The graphs formed by sine and cosine functions...more commonly referred to as waves.
Cosine
The ratio of the adjacent side to the hypotenuse of a right triangle which means adjacent over hypotenuse,
sine
The ratio of the opposite side to the hypotenuse of a right triangle which means opposite over hypotenuse,
Tangent
The ratio of the opposite side to the adjacent side of a right triangle which means opposite over adjacent.
reciprocal
One of two numbers whose product is 1; it is also called multiplicative inverse.
Horizontal shift
Adding a constant to the x-value of a function shifts its graph horizontally.
Vertical shift
Adding a constant to the y-value of a function shifts its graph vertically.
vertical stretch
the parabola appears narrower when y= ax^2 and the absolute value of a is greater than 1
horizontal stretch
All y-coordinates are multiplied by a number less than 1. The points get closer to the x-axis (graph gets fatter).
absolute value
The distance of a number from zero on a number line; shown by | |
Parent (mother) Function
The original or most basic form of a function.
slope
The vertical change over the horizontal change.
Trigonometric Ratios
The comparison of two sides of a right triangle.
Inverse Sine
Domain: [-1,1] Range: [(-pi/2), (pi/2)]
Inverse Cosine
Domain: [-1,1] Range: [0,pi]
Inverse Tangent
Domain: all real numbers Range: ((-pi/2), (pi/2)).
Tangent
Domain: all real numbers besides pi/2+kpi, k is an integer. Range: All real numbers
cotangent
Domain: all real numbers besides kpi, k is an integer. Range: All real numbers.
secant
Domain: all real numbers besides pi/2+kpi, k is an integer. Range: (- infiniti, -1]U[1, infiniti).
cosecant
Domain: all real numbers besides kpi, k is an integer. Range: (-infiniti,-1]U[1, infiniti).