Graph g(t)=4sin(3t)+2 .
Use 3.14 for π .
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
How would I graph this? I have plot the points on the graph but I'm confused
uhm im using it but when i put the function in it said there was a function error
To graph the function g(t) = 4sin(3t) + 2 using the sine tool, you need to follow these steps:
Step 1: Identify the key components of the function:
- Amplitude: The amplitude is the maximum distance the graph reaches above or below the midline. In this case, the amplitude is 4.
- Period: The period is the length of one complete cycle of the graph. The standard period for the sine function is 2π, but since we're using 3.14 for π, the period becomes 2π/3.14 x 3 = 6.
- Vertical shift: The vertical shift is the amount the graph is shifted up or down from the x-axis. In this case, the graph is shifted up by 2 units.
Step 2: Determine the points on the graph:
To graph the function, you need at least two points. The first point should be on the midline, which is the horizontal axis (y = 0). The second point should be either a maximum or minimum value of the graph closest to the first point.
- Midline point: When t = 0, g(t) = 4sin(3(0)) + 2 = 4sin(0) + 2 = 2. So, the first point is (0, 2).
- Maximum/Minimum point: To find the maximum or minimum point closest to the first point, you need to determine the value of t that gives either the maximum or minimum value for the function. In the case of g(t) = 4sin(3t) + 2, the maximum value occurs when sin(3t) is 1, and the minimum value occurs when sin(3t) is -1.
- Maximum point: When sin(3t) = 1, 3t = π/2, and t = π/6.
- Minimum point: When sin(3t) = -1, 3t = 3π/2, and t = π/2.
Step 3: Plot the points and create the graph:
Now that you have the points (0, 2), (π/6, 6), and (π/2, 0), you can plot them on a graph using the x-coordinate for t and the y-coordinate for g(t). Connect the points smoothly to create the graph, following the shape of the sine function.
Remember to label the x-axis as t and the y-axis as g(t). You can also add a scale to the axes to make the graph easier to read and interpret.
With these steps, you should be able to accurately graph the function.
wolframalpha.com is very easy to use. Just type in your function, and it will show the graph. For example,
http://www.wolframalpha.com/input/?i=4sin(3t)%2B2
there is a website called fooplot
you should use it