What is the period of y=3cos(x-7)+2 ? Give an exact value.

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. The period of the basic cosine function, cos(x), is 2π. When the function is of the form cos(Bx), the period is adjusted by the factor B, such that the new period is 2π/B.Function Analysis: In the given function y = 3cos(x - 7) + 2, the coefficient B in front of x is 1 (since there is no coefficient written, it is understood to be 1). This means that the period of the function is the same as the period of the basic cosine function, which is 2π.Final Period Calculation: Therefore, the period of the function y = 3cos(x - 7) + 2 is 2π. The number 3 is the amplitude, -7 is the phase shift, and +2 is the vertical shift. None of these affect the period of the function.

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Q. What is the period of

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

? Give an exact value.

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. The period of the basic cosine function, $\cos(x)$ , is $2\pi$ . When the function is of the form $\cos(Bx)$ , the period is adjusted by the factor $B$ , such that the new period is $\frac{2\pi}{B}$ .
Function Analysis: In the given function $y = 3\cos(x - 7) + 2$ , the coefficient $B$ in front of $x$ is $1$ (since there is no coefficient written, it is understood to be $1$ ). This means that the period of the function is the same as the period of the basic cosine function, which is $2\pi$ .
Final Period Calculation: Therefore, the period of the function $y = 3\cos(x - 7) + 2$ is $2\pi$ . The number $3$ is the amplitude, $-7$ is the phase shift, and $+2$ is the vertical shift. None of these affect the period of the function.