how would i graph
g(x)=4cosx
To graph the function g(x) = 4cos(x), you can follow these steps:
1. Determine the range of values for x that you want to graph. For simplicity, let's assume we want to graph the function over one period, so we choose x values from 0 to 2π.
2. Create a table of values by selecting various x values from the chosen range and calculating the corresponding y values using the function g(x) = 4cos(x). For example, you can select x values like 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4, 2π.
| x | y |
| --- | ----- |
| 0 | 4 |
| π/4 | √2 |
| π/2 | 0 |
|3π/4 | -√2 |
| π | -4 |
|5π/4 | -√2 |
|3π/2 | 0 |
|7π/4 | √2 |
|2π | 4 |
3. Plot the points (x, y) from the table on a coordinate plane. The x-values represent the points on the x-axis, and the y-values represent the corresponding points on the y-axis.
4. Connect the points using a smooth curve. Since the function is periodic, the curve will repeat itself after every 2π. In this case, you will see one complete period of the graph.
5. Label the x-axis with the values you chose, which are multiples of π.
6. Label the y-axis with the values that correspond to the range of y-values you calculated.
The resulting graph will be a sinusoidal curve that oscillates between 4 and -4, crossing the x-axis at π/2 and 3π/2.
To graph the function g(x) = 4cos(x), you can follow these steps:
Step 1: Decide on the range of values for x that you want to graph. For simplicity, let's consider the range from -2π to 2π, which covers a complete period of the cosine function.
Step 2: Determine the key points. Since the amplitude of g(x) is 4, the maximum value of g(x) will be 4 and the minimum value will be -4. Also, the cosine function repeats itself every 2π, so we can mark key points at intervals of 2π.
Step 3: Plot the key points on the graph. Start by marking the x-axis with the key points you determined. Let's start with -2π, -π, 0, π, and 2π.
Step 4: Use the amplitude to determine how far the graph should move up and down from the x-axis. Since the amplitude is 4, you would move 4 units above and below the x-axis, starting from the key points you marked in Step 3.
Step 5: Connect the points with a smooth curve. Since the cosine function is a continuous function, you can draw a continuous curve passing through the key points.
By following these steps, you should be able to graph g(x) = 4cos(x) accurately. Remember to label the axes and provide a title for the graph to make it complete.
Cos(x) is a sinusoidal function with a period of 2π and amplitude 1, i.e. it oscillates between +1 and -1.
You're expected to know the basic graph of cos(x), sin(x) and tan(x).
(see link below for details).
Based on the basic graphs, we can graph the variants. From cos(x), we can graph Acos(x), where A is a numerical constant, which multiplies the amplitude A times. Thus Acos(x) has an amplitude of A.
so g(x)=4cos(x) is simply the graph of cos(x) with an amplitude of 4.
More about graphing sinusoidal functions. Be patient, page 1 is about sin(x), but examples on cos(x) is on page 2 of the link.
http://www.purplemath.com/modules/grphtrig.htm