Answer:
j(x) is shifted right by [tex]\frac{5\pi}{4}[/tex] units
Step-by-step explanation:
Given
[tex]j(x)= 51 cos(x + \frac{\pi}{2})[/tex]
[tex]k(x)= 51 cos(x - \frac{3\pi}{4})[/tex]
Required
Determine the transformation from j(x) to k(x)
The transformation shows a horizontal shift from j(x) to k(x).
First, we need to determine the unit shifter from j(x) to k(x) as follows;
[tex]j(x)= 51 cos(x + \frac{\pi}{2})[/tex]
Express [tex]\frac{\pi}{2}[/tex] as [tex]\frac{5\pi}{4}-\frac{3\pi}{4}[/tex]
So:
[tex]j(x)= 51 cos(x + \frac{\pi}{2})[/tex] becomes
[tex]j(x) = 51cos(x + \frac{5\pi}{4}-\frac{3\pi}{4})[/tex]
Reorder
[tex]j(x) = 51cos(x -\frac{3\pi}{4}+ \frac{5\pi}{4})[/tex]
Comparing this to k(x), we have:
[tex]k(x)= 51 cos(x - \frac{3\pi}{4})[/tex]
In other words:
[tex]k(x) = j(x - \frac{5\pi}{4})[/tex]
This implies that j(x) is shifted right by [tex]\frac{5\pi}{4}[/tex] units
Answer:
its D
Step-by-step explanation:
a shift right 5 π/4 units
