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GRAPHS OF TRIGONOMETRIC FUNCTIONS
6. Consider these two functions:
F(x)-2 cos(x)
G(x)-(2x)
Part I: What are the amplitudes of the two functions? (2 points)
what are the periods of the two functions? (2 points)
Part III: Draw sketches of at least two periods of the two graphs, labeling each of the graphs. You may
have to approximate the critical points of one of the graphs. (8 points)

User Richey
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1 Answer

3 votes

Answer:

Part I:

The amplitude of the function F(x) is 2, since the coefficient of the cosine function is 2.

The amplitude of the function G(x) is not defined since it does not contain any trigonometric functions.

The period of the function F(x) is 2π since the period of the cosine function is 2π.

The period of the function G(x) is π since the function is a linear function with slope 2.

Part III:

To sketch the graph of F(x), we can start by plotting the maximum and minimum values of the cosine function, which are 2 and -2, respectively. Then, we can shift the graph downward by 2 units to obtain the graph of F(x). The resulting graph should look like a cosine graph with amplitude 2, but shifted downward by 2 units. We can repeat this pattern for one period of the function, which is 2π, to obtain the following sketch:

| /\

2 | / \

| / \

| / \

| / \

| / \

_____|_________________________

| 0 π 2π

To sketch the graph of G(x), we can start by plotting the y-intercept, which is 0. Then, we can use the slope of 2 to plot additional points on the graph. Since the period of G(x) is π, we can plot two periods by plotting points at x=0, π/2, π, 3π/2, and 2π. The resulting graph should look like a straight line with slope 2. Here is a sketch of the graph:

|

|

|

4 | /

| /

| /

|/________________________

| 0 π 2π

Note that the critical point of G(x) is at x=0, where the slope changes from positive to negative.

User Fernando Gm
by
7.6k points

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