Answer:
a. 1/2
b.
[tex] \frac{2\pi}{3} [/tex]
c.
[tex] - \pi[/tex]
d.
[tex] - 3[/tex]
Step-by-step explanation:
For a function
[tex]y = a \cos (bx - c) + d[/tex]
The amplitude is
[tex] |a| [/tex]
The period is
[tex] \frac{2\pi}{ |b| } [/tex]
and the phase shift is
[tex]x - c[/tex]
And d is the vertical shift
Here we have
[tex]y = \frac{1}{2} \cos(3x + 3\pi) - 3[/tex]
The a amplitude is
[tex] | \frac{1}{2} | = \frac{1}{2} [/tex]
To find the period, first factor out 3 from the
parenthesis
[tex] \frac{1}{2} \cos(3(x + \pi) - 3[/tex]
[tex] \frac{1}{2} \cos(3(x - ( - \pi) ) - 3[/tex]
To find period, the period is
[tex] \frac{2\pi}{3} [/tex]
The phase shift is c so here the phase shift
is
[tex] - \pi[/tex]
or pi units to the left.
Here the vertical shift is -3
