Find the period and, where appropriate, the amplitude of the following function:
y=2sin(x)
Look at my post 10 down from this one, and let me know what you get.
i figured out that the amplitude is 2
as for the period, I'm note sure
would the period then be 2pi because k equals 1?
yes
To find the period and amplitude of the function y = 2sin(x), we need to understand the properties of the sine function.
The general form of the sine function is y = A*sin(Bx + C) + D, where:
- A represents the amplitude, which is the maximum distance the function reaches from its horizontal midline.
- B determines the period, which is the length of one complete cycle of the function.
- C represents the phase shift, which indicates any horizontal shift of the function.
- D is the vertical shift, which moves the function up or down.
In the given function y = 2sin(x), we can observe that:
- The coefficient in front of the sine function, 2, represents the amplitude. In this case, the amplitude is 2.
- The coefficient of x is 1, indicating that the period of the function is 2π or 360 degrees. This means that the function completes one full cycle every 2π units or 360 degrees.
Therefore, the period of the function y = 2sin(x) is 2π, and the amplitude is 2.