4. Graphing Trigonometric Functions

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sin 5x

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + cos 2x

Match each function with its graph in choices A–I. (One choice will not be used.)

y = cos (x - π/4)

A. <IMAGE> B. <IMAGE> C. <IMAGE>

D. <IMAGE> E. <IMAGE> F. <IMAGE>

G. <IMAGE> H. <IMAGE> I. <IMAGE>

In Exercises 53–60, use a vertical shift to graph one period of the function. y = −3 sin 2πx + 2

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −4 sin 3π/2 t

In Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4. y = cos πx + sin π/2 x

For the topic of graphs of the sine and cosine functions, what is the axis of symmetry for the graph of $y=\left|x\right|$?

In Exercises 53–60, use a vertical shift to graph one period of the function. y = cos x + 3

Given the graphs of $y=\sin \left(x\right)$ and $y=\cos \left(x\right)$, which of the following points lies on the y-axis and is also on the line that passes through the point $(0,1)$ and is parallel to the line passing through points $(0,0)$ and $(\pi ,0)$?

In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 3 cos(2x − π)

Fill in the blank(s) to correctly complete each sentence.

The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x ______ unit(s) to the ________ (right/left).

In Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = 4 cos 2πx

Graph each function over a two-period interval.

y = sin (x + π/4)