Answer:
The graph is shown below.
Step-by-step explanation:
The trigonometric expression is:
[tex]f(x)=sin\ (x)-5[/tex]
The general form is:
[tex]f(x)=a\ \text{sin}\ (bx-c)+d[/tex]
Comparing the two expression we know:
a = 1
b = 1
c = 0
d = -5
Compute the value of amplitude, |a | as follows:
[tex]\text{Amplitude}=|a|=|1|=1[/tex]
Compute the period of the function as follows:
[tex]\text{Period}=\frac{2\pi}{|b|}=\frac{2\pi}{|1|}=2\pi[/tex]
Compute the phase shift as follows:
[tex]\text{Phase Shift }=\frac{c}{b}=\frac{0}{1}=0[/tex]
The vertical shift is:
[tex]\text{Vertical Shift}=d=-5[/tex]
The properties of the trigonometric function are:
Amplitude = 1
Period = 2π
Phase shift = 0
Vertical shift = -5
Plot the graph of the trigonometric function by selecting a few points.
x : [tex]0[/tex] [tex]\frac{\pi}{2}[/tex] [tex]\pi[/tex] [tex]\frac{3\pi}{2}[/tex] [tex]2\pi[/tex]
f (x) : -5 -4 -5 -6 -5
The graph is shown below.
