What is the period of y=3cos(x-7)+2 ? Give an exact value. Choose 1 answer: (A) 2π (B) π (C) 2π/3 (D) π/2

Period Determination: The period of a cosine function, y = A*cos(Bx - C) + D, is determined by the coefficient B in front of the x variable inside the cosine function. The period of the basic cosine function, cos(x), is 2π. When the function is of the form cos(Bx), the period is given by the formula 2π/B. In our function, y = 3cos(x - 7) + 2, the coefficient B is 1 because the function can be written as cos(1*(x - 7)).Coefficient B: Since the coefficient B is 1, the period of y = 3cos(x - 7) + 2 is the same as the period of the basic cosine function, which is 2π. The other parameters, A, C, and D, which are 3, -7, and 2 respectively, do not affect the period of the function.Calculation for Period: Therefore, the period of the function y = 3cos(x - 7) + 2 is 2π. This corresponds to answer choice (A).

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Calculus

Find derivatives of sine and cosine functions

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Q. What is the period of

y=3\cos(x-7)+2

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Give an exact value.

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Choose

1

answer:

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(A)

2\pi

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(B)

\pi

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(C)

\frac{2\pi}{3}

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(D)

\frac{\pi}{2}

Period Determination: The period of a cosine function, $y = A\cos(Bx - C) + D$ , is determined by the coefficient $B$ in front of the $x$ variable inside the cosine function. The period of the basic cosine function, $\cos(x)$ , is $2\pi$ . When the function is of the form $\cos(Bx)$ , the period is given by the formula $\frac{2\pi}{B}$ . In our function, $y = 3\cos(x - 7) + 2$ , the coefficient $B$ is $1$ because the function can be written as $B$ $0$ .
Coefficient B: Since the coefficient $B$ is $1$ , the period of $y = 3\cos(x - 7) + 2$ is the same as the period of the basic cosine function, which is $2\pi$ . The other parameters, $A$ , $C$ , and $D$ , which are $3$ , $-7$ , and $2$ respectively, do not affect the period of the function.
Calculation for Period: Therefore, the period of the function $y = 3\cos(x - 7) + 2$ is $2\pi$ . This corresponds to answer choice (A).