4. Graphing Trigonometric Functions

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

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 $(\pi ,0)$?

Graph each function over a two-period interval.

y = cos (x - π/2 )

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

The graph of y = sin (x + π/4) is obtained by shifting the graph of y = sin x ______ unit(s) to the ________ (right/left).

An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.

𝒮(t) = 5 cos 2t

What is the frequency?

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = -2 cos 3x

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

y = -½ cos 3x

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

y = sin (x - π/4)

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

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

In Exercises 31–34, determine the amplitude of each function. Then graph the function and y = cos x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 2 cos x

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 = 10 cos 2πt

Sketch the function $y=\(\cos\]\left\)(x\(\right\))-1$ on the graph below.