Question

Use the graph of y=sin x to graph one cycle of the function f(x)=sin(1/2x). Indicate the amplitude, period, and the phase shift.

Answer 1

Period of the sine function is 2pi whenever the coefficient of x or theta is 1. To get the period when there is a 1/2 in front of the x or theta, you simply divide 2pi by that coefficient to get the new period for that sine function. Amplitude is just the the max value of the function - minimum value. Here the maximum that sin(1/2x) reaches is 1 and it's minimum is at -1 so amplitude = 1 - (-1) = 2. There is no phase-shift because the function is not being translated right or left, or being multiplied by any value or anything so we don't worry about that.

Period = 2pi / (1/2) = 4pi
Amplitude = 1 - (-1) = 2
Phase-shift : none