Question

1. Find the phase shift of the function y = 5cos(2x + pi/2).

2. Which of the following functions has a maximum y value of 4?

y = 4cosx
y = cos4x
y = cosx + 4
y = cos(x + 4)

Answer 1

see explanation

Explanation:

1

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period =
`(2\pi )/(b)` and

phase shift = -
`(c)/(b)`

here b = 2 and c =
`(\pi )/(2)`, thus

phase shift = -
`((\pi )/(2) )/(2)` = -
`(\pi )/(4)`

2

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4