Respuesta :
Answer:
Step-by-step explanation:
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The period is 4. The relationship between period and b (the coefficient of the independent variable of the cosine function) is (period) =(2π.b). Given that the period here is 4,
2π 2π
4 = ---------, and so b = ------- = π/2.
4
So now our y = a*cos (bx + c) becomes
π
y = 10*cos (------x + 0 + 10
2
The horizontal center line of this cosine curve is y = 10. The maximum value of the curve is 20, which is 10 + 10, and the minimum value is 0, which is 10 - 10.
The function that describes the given situation is [tex]\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10[/tex] and this can be determined by using the properties of the trigonometric function.
Given :
- A cosine function has a period of 4, a maximum value of 20, and a minimum value of 0.
- The function is not a reflection of its parent function over the x-axis.
The following steps can be used in order to determine the function could be the function described:
Step 1 - According to the given data, the cosine function has a period of 4.
Step 2 - Now, the independent variable of the cosine function is given by:
[tex]\rm 4b = 2\pi[/tex]
[tex]\rm b =\dfrac{\pi}{2}[/tex]
Step 3 - The maximum value of the cosine function is 1 and the minimum value of the cosine function is -1.
Step 4 - From the above steps, the function that described the given situation is given by:
[tex]\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10[/tex]
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/21286835
