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vitfil [10]
3 years ago
5

Review the given functions. j (x) = 51 cosine (x + StartFraction pi Over 2 EndFraction) + 24 k (x) = 51 cosine (x minus StartFra

ction 3 pi Over 4 EndFraction) + 24 What is the transformation of function j(x) to function k(x)? a shift left StartFraction pi Over 4 EndFraction units a shift left StartFraction 5 pi over 4 EndFraction units a shift right StartFraction pi Over 4 EndFraction units a shift right StartFraction 5 pi over 4 EndFraction units
Mathematics
2 answers:
son4ous [18]3 years ago
6 0

Answer:

j(x) is shifted right by \frac{5\pi}{4} units

Step-by-step explanation:

Given

j(x)= 51 cos(x + \frac{\pi}{2})

k(x)= 51 cos(x - \frac{3\pi}{4})

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;

j(x)= 51 cos(x + \frac{\pi}{2})

Express \frac{\pi}{2} as \frac{5\pi}{4}-\frac{3\pi}{4}

So:

j(x)= 51 cos(x + \frac{\pi}{2}) becomes

j(x) = 51cos(x + \frac{5\pi}{4}-\frac{3\pi}{4})

Reorder

j(x) = 51cos(x -\frac{3\pi}{4}+ \frac{5\pi}{4})

Comparing this to k(x), we have:

k(x)= 51 cos(x - \frac{3\pi}{4})

In other words:

k(x) = j(x - \frac{5\pi}{4})

<em>This implies that j(x) is shifted right by </em>\frac{5\pi}{4}<em> units</em>

Otrada [13]3 years ago
4 0

Answer:

its D

Step-by-step explanation:

a shift right 5 π/4 units

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