Question

graph the following function over a two - period interval. give the period and the amplitude.

( y = sin \frac { 1 } { 5 } x )

the period of the function ( y = sin \frac { 1 } { 5 } x ) is
(simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any n

the amplitude of the function ( y = sin \frac { 1 } { 5 } x ) is
(type an integer or a simplified fraction.)

which of the following is the correct graph of the function ( y = sin \frac { 1 } { 5 } x? )

a.
b.

Explanation:

Step1: Recall the formula for the period of \(y = A\sin(Bx)\)

The period of a sine function \(y = A\sin(Bx)\) is given by \(T=\frac{2\pi}{|B|}\). For the function \(y=\sin(\frac{1}{5}x)\), here \(B = \frac{1}{5}\).

$$T=\frac{2\pi}{\frac{1}{5}}=10\pi$$

Step2: Recall the formula for the amplitude of \(y = A\sin(Bx)\)

The amplitude of a sine function \(y = A\sin(Bx)\) is given by \(|A|\). For the function \(y=\sin(\frac{1}{5}x)\), here \(A = 1\). So the amplitude \(|A|=1\)

Answer:

The period of the function \(y = \sin\frac{1}{5}x\) is \(10\pi\).
The amplitude of the function \(y=\sin\frac{1}{5}x\) is \(1\).