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4.5 - 4.8 Vocabulary: Graphing Trigonometric Functions

                                    Name: ___________________
                                    Period: __________________
                                    Date: ____________________
Across
You can see that the _________ function has vertical asymptotes when sin x is zero, which occurs at x = n*pi, where n is an integer.
The _______ sine function is defined by y = arcsin x if and only if sin y = x.
You can use graphs of trigonometric functions to model real-life situations, such as the ________ from a television camera to a unit in a parade.
The graph of the sine function is a sine _____
Along with the sine function, recall that the _______ is also odd. That is, f(-x) = -f(x).
When cos x = 0, the __________ does not exist.
Recall that for a function to have an inverse function, it must be one-to-one--that is, it must pass the Horizontal Line ____.
You can define an inverse tangent function by ____________ the domain of y = tan x to the interval (-pi/2, pi/2).
The cosine curve is symmetric with respect to the _-_____.
The constant c in the general equations y = a sin (bx - c) and y = a cos (bx - c) creates horizontal ____________ (shifts) of the basic sine and cosine curves.
The sine curve is symmetric with respect to the _______.
The graph of y = (1/2)cox x is a vertical ______ of the graph of y = cos x.
Note that when 0 < b < 1, the period of y = a sin bx is greater than 2pi and represents a __________ stretching of the graph of y = a sin x. Similarly, when b > 1, the period of y = a sin bx is less than 2pi and represents a __________ shrinking of the graph of y = a sin x.
The ______ of y = a sin bx and y = a cos bx is given by P = (2pi/b) where b is a positive real number.
You can graph a _______ of two functions using properties of the individual functions.
A point that moves on a coordinate line is in simple ________ motion when its distance d from the origin at time t is given by d = a sin wt or d = a cos wt where a and w are real numbers such that w > 0.
The ______ of the sine and cosine functions is the set of all real numbers.
Number of cycles per second
Down
The period of the function represents one _____
The graph of y = tan x has vertical ___________ at x = pi/2 and x = -pi/2 and occur at x = pi/2 + n*pi, where n is an integer.
In comparing the graphs of the cosecant and secant functions with those of the sine and cosine functions, respectively, note that the "hills" and "_______" are interchanged.
As with the trigonometric functions, much of the work with the inverse trigonometric functions can be done by ______ calculations, rather than by calculator approximations.
_________ translations are caused by the constant d in the equations d + a sin (bx - c) and y = d + a cos (bx - c)
You can use sine and cosine functions in scientific calculations, for instance, to model the airflow of your respiratory cycle.
_____ triangles often occur in real-life situations, for example, to analyze the design of a new slide at a water park.
In the function f(x) = x*sin x, the factor x is called the _______ factor.
Sine and cosine functions have a period of 2__.
The graph of y = -f(x) is a ___________ in the x-axis of the graph of y = f(x).
In surveying and navigation, directions can be given in terms of ________.
The ______ of sine and cosine functions is the interval [-1, 1].
Since the cosine function is symmetric with respect to the y-axis, it follows that the function is ____.
The _________ of y = a sin x and y = a cos x represents half the distance between the maximum and minimum values of the function.
The graph of y = 3 cos x is a vertical _______ of the graph of y = cos x.
To sketch the basic sine and cosine functions by hand, it helps to note five ___ points in one period of each graph: intercepts, maximum points, and minimum points.
You can use an inverse trigonometric function to model the angle of _________ from a television camera to a space shuttle launch.
The number c/b for y = a sin (bx - c) and y = a cos (bx - c) is the _____ shift.
Since the sine curve is symmetric with respect to the origin, it follows that the function is ___.