QUESTION 1
The given trigonometric function is
[tex]y=0.5\cos(3x)[/tex]
The amplitude of this function is 0.5 while the amplitude of the parent function [tex]y=\cos(x)[/tex] is 1.
The period of this function is [tex]\frac{2\pi}{3}[/tex] while the parent function is [tex]\2pi[/tex]
This function will complete two periods on the interval [tex][0,\frac{4\pi}{3}][/tex]
We plot some few points as shown on the graph and draw our curve through it.
QUESTION 2
The given function is
[tex]y=-2\sin(\frac{2\pi}{3}x)[/tex]
This function has a period of 3 while the corresponding basic function, [tex]y=\sin(x)[/tex] has a period of [tex]2\pi[/tex]
The amplitude of this function is 2 while that of the corresponding basic function is 1.
This function is reflected in the x-axis because of the negative a value.
We plot some few points and draw the graph as shown in the graph
QUESTION 3
The given function is
[tex]y=4\sin(3\pi x)-2[/tex]
This function has an amplitude of 4 as compared to the amplitude of the basic sine which is 1.
It has a period of [tex]\frac{2}{3}[/tex] and shifted vertically 2 units down.
We plot some few points as shown in the graph and draw our graph through.
