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 $\pi$ 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
Final Answer: The period of the function \(y=\cos \frac{1}{6} x\) is \(\boxed{12\pi}\) and the amplitude of the function is \(\boxed{1}\).
Step 1 ：The period of a cosine function is given by \(\frac{2\pi}{|b|}\) 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 \(\frac{2\pi}{|\frac{1}{6}|} = 12\pi\).
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 \(\boxed{12\pi}\) and the amplitude of the function is \(\boxed{1}\).
