Determine the number of cycles the sine function shown to the right has in the interval from 0 to 2π. Find the amplitude and the period of the function.

Question

Determine the number of cycles the sine function shown to the right has in the interval from 0 to 2π. Find the amplitude and the period of the function.

Answer 1

One cycle of a sine wave goes from 0 to 1 to -1 and back to 0 on the y-axis. In this graph, the function does it 4 times between 0 and 2π, so there are four cycles. The period would then be 2π/4 or π/2. The amplitude is the distance from zero to the maximum height. In this case, the amplitude is 5.