Question

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

Answer 1

`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)`