Identify the amplitude and period of the following functions.
$f\left(\pi\right)=2\sin2\theta$

Verified step by step guidance

1. Identify the general form of the sine function, which is \( f(\theta) = a \sin(b\theta) \), where \( a \) is the amplitude and \( \frac{2\pi}{b} \) is the period.
2. In the given function \( f(\theta) = 2\sin(2\theta) \), compare it with the general form to identify the values of \( a \) and \( b \). Here, \( a = 2 \) and \( b = 2 \).
3. The amplitude of a sine function is the absolute value of \( a \). Therefore, the amplitude is \( |2| = 2 \).
4. The period of a sine function is calculated using the formula \( \frac{2\pi}{b} \). Substitute \( b = 2 \) into the formula to find the period.
5. Calculate the period: \( \frac{2\pi}{2} = \pi \). Thus, the period of the function is \( \pi \).