Question

A wave is modeled with the function y = 1/2 sin 3 theta. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis.

Answer 1

It is a sinusoidal graph, which oscilates around the x-axis (y=0), from y = -0.5 to y = 0.5

General description (as reference)
It passes through the origin (0,0), increases until the max value (y = 0.5) when x = π6, then start to decrease,  crosses the x-axis x = π/3, continues decreasing until the min value (y = -0.5) when x = 2π/3, then it starts to increase, crossing the x-axis again at x = 2π/3, and the pattern repeats indefinetely to the right of x = 2π/3 and to the left of x = 0.

 Specific description:

Amplitud: 0.5----> the coefficient in front of the sine function

Period: 2π/3 ----> 2π divided by the coefficient in front of the argument (3)

Points of intersection with the x-axis: 0 + /- nπ/3, with n = 0,1,2,3,.....

Type of function: odd

Maximun value: 1/2

Minimum value: -1/2