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find the amplitude and the period for ( y = 5 sin 2 x ). write the period as an exact value involving ( pi ).
amplitude:
period:

Explanation:

Step1: Recall the formula for the period of a sine function

The general form of a sine function is \(y = A\sin(Bx + C)+D\). The period \(T\) is given by the formula \(T=\frac{2\pi}{|B|}\).

Step2: Identify the value of \(B\) in the given function

For the function \(y = 5\sin(2x)\), we have \(B = 2\).

Step3: Calculate the period

Substitute \(B = 2\) into the period formula \(T=\frac{2\pi}{|B|}\). Since \(|2|=2\), we get \(T=\frac{2\pi}{2}=\pi\).

Answer:

Period: \(\pi\)