To determine the amplitude of the function [tex]\( y = \frac{1}{2} \sin(2x) \)[/tex], let's go through the properties of a sine function.
The general form of a sine function is:
[tex]\[ y = A \sin(Bx + C) \][/tex]
Where:
- [tex]\( A \)[/tex] represents the amplitude.
- [tex]\( B \)[/tex] affects the period of the sine wave.
- [tex]\( C \)[/tex] represents the phase shift.
The amplitude of a sine function is the absolute value of the coefficient [tex]\( A \)[/tex] in front of the sine function. The amplitude tells us how far the peaks and the troughs of the sine wave reach from the central axis (y = 0).
In the given function [tex]\( y = \frac{1}{2} \sin(2x) \)[/tex], the coefficient [tex]\( A \)[/tex] in front of the sine function is [tex]\( \frac{1}{2} \)[/tex].
Therefore, the amplitude of the function [tex]\( y = \frac{1}{2} \sin(2x) \)[/tex] is:
[tex]\[ \text{Amplitude} = \left| \frac{1}{2} \right| = \frac{1}{2} \][/tex]
Thus, the correct answer is:
A. [tex]\(\frac{1}{2}\)[/tex]
