Question

A function is represented by y = cos (2π/5)x - 1. Determine the amplitude and period of the function. What is the equation of the midline?

A) amplitude is 1; period is 5; y = 0
B) amplitude is 1; period is 2/5; y = 1
C) amplitude is 1; period is 5; y = −1
D) amplitude is 1; period is 2π; y = −1

(Please explain how you get it)

Answer 1

Given that: y = cos(2pi/5)x -1

The general form of cos function is y = A cos(Bx+C) +D

So amplitude = A=1

Period = 2pi/B=2pi/(2pi/5)= 5

Phase shift = -C/B= 0

Vertical shift = D=-1

So the equation of the midline is y=-1

Sot he correct option is C.

Answer 2

The cosine equation is

y = Acos(Bx+C) +D

Comparing

y = cos (2π/5)x-1

We get A= 1

The amplitude of the function is 1.

Now period = 2π/B = 2π/(2π/5)=5

Now the Mid line equation for the cosine function is y =0

Here as the shift D = -1.

The mid line equation shifts one unit down.

Hence the mid line equation is y = -1

So the Amplitude is 1, period is 5 & the mid line equation is y = -1

Option C) is the right answer