Question

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

Answer 1

Answer:

$Amplitude = /\frac{3}{2}/$

$Range = [\frac{-3}{2} , \frac{3}{2}]$

$Period = \pi$

Step-by-step explanation:

Given: $y = \frac{3}{2}cos\frac{t}{2}$

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 :

$Period =\frac{2\pi }{B}$

$B = \frac{1}{2}$

Therefore , with the comparison

$A = /\frac{3}{2}/$

which means that:

$Range = \frac{-3}{2} , \frac{3}{2}$

$Period = \frac{2\pi }{2}$

$Period = \pi$