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Snowcat [4.5K]
3 years ago
6

A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shif

t is 9 units down, and the period of the function is 7pi/12. The graph of the function does not show a phase shift. What is the equation of the cosine function described?
Fill in the blanks using values from this list: -20, -11, -9, -2, 2, 9, 11, 20, 7pi/12,12pi/7,7/24,24/7

f(x)=___cos(_____x)______
Mathematics
1 answer:
omeli [17]3 years ago
7 0

We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is \frac{7\pi}{12}. The graph of the function does not show a phase shift. We are asked to write the equation of our function.

We know that general form a cosine function is y=A\cos(b(x-c))-d, where,

A = Amplitude,

\frac{2\pi}{b} = Period,

c = Horizontal shift,

d = Vertical shift.    

The equation of parent cosine function is y=\cos(x). Since function is reflected about x-axis, so our function will be y=-\cos(x).

Let us find the value of b.

\frac{2\pi}{b}=\frac{7\pi}{12}

7\pi\cdot b=24\pi

\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}

b=\frac{24}{7}

Upon substituting our given values in general cosine function, we will get:

f(x)=-11\cos(\frac{24}{7}x)-9

Therefore, our required function would be f(x)=-11\cos(\frac{24}{7}x)-9.

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