Question

Find the period, range, and amplitude of the cosine function y= 3/2cos t/2

Answer 1

`Amplitude = /(3)/(2)/`

`Range = [(-3)/(2) , (3)/(2)]`

`Period = \pi`

Explanation:

Given:
`y = (3)/(2)cos(t)/(2)`

Comparing the equation with the standard form of cosine function :

`y = A cos(Bx- C)`

where:

`A = Amplitude`

Formula for calculating Amplitude is given as:

`Amplitude = /A/`

The formula for calculating Period is given as :

`Period =(2\pi )/(B)`

`B = (1)/(2)`

Therefore , with the comparison

`A = /(3)/(2)/`

which means that:

`Range = (-3)/(2) , (3)/(2)`

`Period = (2\pi )/(2)`

`Period = \pi`