What is the period of y = 2sin(x)?

The period of \( y = 2\sin(x) \) is \( 2\pi \).

In trigonometry, the period of a sine function is the length of the interval over which the function completes one full cycle. For the basic sine function \( \sin(x) \), the period is \( 2\pi \). This means that the function repeats its values every \( 2\pi \) units along the x-axis.

When we look at the function \( y = 2\sin(x) \), the coefficient 2 in front of the sine function affects the amplitude, not the period. The amplitude is the maximum value the function reaches, and in this case, it is 2. However, the period remains unchanged because the period of a sine function is determined by the coefficient of \( x \) inside the sine function, not the coefficient outside.

To summarise, the period of \( y = 2\sin(x) \) is the same as the period of \( \sin(x) \), which is \( 2\pi \). This means that the function \( y = 2\sin(x) \) will repeat its pattern every \( 2\pi \) units along the x-axis. Understanding this concept is crucial for analysing and graphing trigonometric functions effectively.