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RichardKing2376
27.11.2019 •
Mathematics
consider the graph of the cosine function shown below.
a. find the period and amplitude of the cosine function.
b. at what values of θ for 0 ≤ θ ≤ 2π do the maximum value(s), minimum values(s), and zeros occur?
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Ответ:
a.
Period = π
Amplitude = 4
b.
Maximum at: x = 0, π and 2π
Minimum at: x = π/2 and 3π/2
Zeros at: x = π/4, 3π/4, 5π/4 and 7π/4
Step-by-step explanation:
Part a:
Amplitude represents the half of the distance between the maximum point and the minimum point of the function. So the easy way to find the amplitude is: Find the difference between maximum and minimum value of the function and divide the difference by 2.
So, amplitude will be:![\frac{Maximum-Minimum}{2}=\frac{4-(-4)}{2}=\frac{8}{2}=4](/tpl/images/0393/0981/f98ee.png)
Therefore, the amplitude of the function is 4.
Period is the time in which the function completes its one cycle. From the graph we can see that cosine started at 0 and completed its cycle at π. After π the same value starts to repeat. So the period of the given cosine function is π.
Part b:
From the graph we can see that the maximum values occur at the following points: x = 0, π and 2π
The scale on x-axis between 0 and π is divided into 4 squares, so each square represents π/4
Therefore, the minimum value occurs at x = π/2 and 3π/2
Zeros occur where the graph crosses the x-axis. So the zeros occur at the following points: π/4, 3π/4, 5π/4 and 7π/4
Ответ:
we know that
The distance of the point (7, 8.75) to the x-axis (the horizontal line) is 8.75
then
case A) (-7, 5.25)---------> is not correct ( the distance to the x-axis is 5.25)
case B) (8.75, 6)---------> is not correct ( the distance to the x-axis is 6)
case C) (6, -8.75)---------> is correct ( the distance to the x-axis is 8.75)
the answer is the option C) (6, -8.75)