Question 1179574: The graphs of the height h and thehorizontal displacement p of the red saw tooth areexamples of sine and cosine curves, respectively.Draw y = sinx and y = cosx on a graphing tool andcompare them with the graphs that you drew in thepreceding exercises. Use these graphs to answer thefollowing questions:(a)For what values of t is the red tooth 0.8 feetabove the table? 0.8 feet below the table?(b)When is the tooth 6 inches to the right of thevertical axis? When is it farthest left?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Okay, let's analyze the sine and cosine graphs and answer the questions about the red saw tooth's position.
**Comparing Graphs**
You're right, the graphs of the height (h) and horizontal displacement (p) of the red saw tooth resemble sine and cosine curves, respectively. Here's a comparison:
* **Height (h):** The height graph is similar to a sine curve because it starts at the midline (average height), goes up to a maximum, then back down to the midline, then to a minimum, and finally back to the midline. This is the characteristic shape of a sine wave.
* **Horizontal Displacement (p):** The horizontal displacement graph is similar to a cosine curve because it starts at a maximum (farthest to the right), then goes to the midline, then to a minimum (farthest to the left), back to the midline, and finally back to the maximum. This is the characteristic shape of a cosine wave.
**Using Graphs to Answer Questions**
To answer the specific questions about the red tooth's position, we need to make some assumptions about the saw blade's rotation speed and the starting position of the tooth. Let's assume:
* **Rotation Speed:** The saw blade completes one full rotation every 60 seconds (period = 60 seconds).
* **Starting Position:** The red tooth starts at its highest point.
Based on these assumptions, we can sketch the graphs of h(t) and p(t):
**a) Height (h)**
* **0.8 feet above the table:** This corresponds to a y-value of 0.8 on the sine graph. Using a graphing tool or a sine table, we find that sin(x) = 0.8 at approximately x = 53.1 degrees and x = 126.9 degrees. Since the period is 60 seconds, these angles correspond to t = 8.85 seconds and t = 21.15 seconds. Due to the periodic nature of the sine function, the tooth will be 0.8 feet above the table at these times during each rotation.
* **0.8 feet below the table:** This corresponds to a y-value of -0.8 on the sine graph. We find that sin(x) = -0.8 at approximately x = 233.1 degrees and x = 306.9 degrees, which correspond to t = 38.85 seconds and t = 51.15 seconds during each rotation.
**b) Horizontal Displacement (p)**
* **6 inches to the right:** This corresponds to a y-value of 0.5 feet on the cosine graph (since 6 inches = 0.5 feet). We find that cos(x) = 0.5 at approximately x = 60 degrees and x = 300 degrees, which correspond to t = 10 seconds and t = 50 seconds during each rotation.
* **Farthest left:** The tooth is farthest left when the cosine graph reaches its minimum value of -1. This occurs at x = 180 degrees, which corresponds to t = 30 seconds during each rotation.
**Important Notes**
* The exact values of t will depend on the assumed rotation speed and starting position.
* The graphs of sine and cosine are periodic, so the tooth will repeatedly reach the same positions over time.
* Using a graphing tool can help visualize the positions and make it easier to find the corresponding times.
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
In this post, key necessary input data are missed, due to the author's negligence.
So, the problem is DEFECTIVE: it is mutilated and cannot be solved.
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