Graph the following function over a two-period interval. Give the period and the amplifude.
$y = \cos \frac{1}{6} x$
What is the period of the function $y = \cos \frac{1}{6} x$ ?
(Simplify your answer. Type an exact answer, using $π$ as needed. Use integers or fractions for any numbers in the expression.)
What is the amplitude of the function $y = \cos \frac{1}{6} x$ ?
(Type an integer or a simplified fraction.)
Which of the following is the correct graph of the function $y = \cos \frac{1}{6} x$ ?
A.
B.
C.
D.

Answer

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Final Answer: The period of the function $y = \cos \frac{1}{6} x$ is $12 π$ and the amplitude of the function is $1$ .

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Step 1 ：The period of a cosine function is given by $\frac{2 π}{| b |}$ where $b$ is the coefficient of $x$ inside the cosine function. In this case, $b = \frac{1}{6}$ .

Step 2 ：The amplitude of a cosine function is the absolute value of the coefficient of the cosine function, which in this case is 1.

Step 3 ：So, the period of the function $y = \cos \frac{1}{6} x$ is $\frac{2 π}{| \frac{1}{6} |} = 12 π$ .

Step 4 ：The amplitude of the function is $1$ .

Step 5 ：Final Answer: The period of the function $y = \cos \frac{1}{6} x$ is $12 π$ and the amplitude of the function is $1$ .

Answer

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