Write an equation of the cosine function with amplitude pi/2 and period 3

Question

asked Mar 28, 2021 149k views

1 Answer

Charlie Kee · Answer 1 · 2021-04-02T17:45:08+0000

Answer:

$y = (\pi)/(2)cos((2\pi)/(3)x)$

Explanation:

Given

$Amplitude = (\pi)/(2)$

Period = 3

Required

Write the equivalent cosine function

The general formula is:

y = acos(bx)

Where

amplitude = |a|

$period = (2\pi)/(b)$

Substitute
$(\pi)/(2)$ for amplitude in
amplitude = |a|

$|a| = (\pi)/(2)$

$a = (\pi)/(2)$

Substitute 3 for period in
$period = (2\pi)/(b)$

$(2\pi)/(b) = 3$

Multiply both sides by b

$2\pi = 3b$

Divide through by 3

$b = (2\pi)/(3)$

Hence;

y = acos(bx) becomes

$y = (\pi)/(2)cos((2\pi)/(3)x)$