I frequently find myself lost with concepts in math, and even looking at some problems is an anxiety trip.
I have several questions on a test, all vaguely revolving around the same concept, but I'm not sure how to make sense of them. Could someone explain how to complete these problems and graph them?
The "sine tool" that it mentions is just a graph provided to make the points on, unfortunately I cannot create links or images.
I'm not necessarily looking for someone to "do my homework for me," but would appreciate someone walking me through each of these problems so I can see how the concepts apply to each of them. I appreciate any help.
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1. A sine function has the following key features:
Frequency = 1/4π
Amplitude = 2
Mid-line: y = 2
y-intercept: (0, 2)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point."
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2. A sine function has the following key features:
Period = 4
Amplitude = 3
Mid-line: y=−1
y-intercept: (0, -1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point.
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3. A sine function has the following key features:
Period = π
Amplitude = 2
Mid-line: y=−2
y-intercept: (0, -2)
The function is a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point.
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4. A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation the weight was at its highest point. From its resting position, it takes 12 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and the highest points is 10 in. Assume the resting position is at y = 0.
Use the sine tool to graph the function. The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point.
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5. At an ocean depth of 20 meters, a buoy bobs up and then down 2 meters from the ocean's depth. Four seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0, the buoy is at normal ocean depth.
Use the sine tool to graph the function. The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point.
Have you studied the solutions that have already been provided?
I'm not sure what you mean, if you're implying have I studied this material before, then no. It's a new concept, and even concepts that I learn in the past are quick to slip past me or be forgotten, so I'm really at a loss with what to do, the explanations and reading material provided by the instructor lead me to being more confused than enlightened.
You posted these problems earlier, and several were solved in some detail. Have you checked those solutions?
Sure! I can help you understand how to complete these problems and graph them. Let's start with the first problem:
1. The key features given in this problem are:
- Frequency = 1/4π
- Amplitude = 2
- Mid-line: y = 2
- y-intercept: (0, 2)
- The function is not a reflection of its parent function over the x-axis.
To graph this function, we can start by understanding what each of these key features means. The frequency of a sine function determines how many complete cycles occur within a certain interval. In this case, the frequency is 1/4π, which means that one complete cycle occurs in a 4π interval.
The amplitude determines the height of the peaks and valleys of the sine curve. In this case, the amplitude is 2, so the highest point will be 2 units above the mid-line (y = 2), and the lowest point will be 2 units below the mid-line.
Now, to graph the function using the given sine tool, we need to find the points that satisfy the given conditions. The first point must be on the mid-line, so (0, 2) is already given as the y-intercept. The second point must be a maximum or minimum value on the graph closest to the first point.
Since the function is not a reflection over the x-axis, the first point will be a maximum value on the graph. This means that the second point will be a minimum value on the graph closest to (0, 2). To find this point, we need to determine how much the function has shifted horizontally (phase shift). Since no information about the phase shift is given, we can assume it is zero.
Based on the frequency and amplitude, we can determine that the period (length of one cycle) is 4π. Therefore, the second point will be at (4π/4, 2 - 2) = (π, 0).
Now we have the first two points: (0, 2) and (π, 0). We can plot these points on the sine tool and connect them to create the graph of the function.
Repeat this process for the remaining problems, applying the given key features to determine the frequency, amplitude, mid-line, and the first two points on the graph. Remember to consider whether the function is a reflection of its parent function over the x-axis.
I hope this explanation helps you understand how to tackle these problems and graph the sine functions. If you have any further questions, feel free to ask!