Question

A graph of f(x)=acos(bx) is shown, where b is a positive constant. Determine the values of a and b.

Answer 1

Option (1)

Explanation:

Equation of the given wave function,

f(x) = acos(bx)

Here, a = amplitude of the wave

Period of the wave =
`(2\pi )/(B)`

From the graph attached,

Amplitude =
`(4-(-4))/(2)`

=
`(4+4)/(2)`

= 4

Period of the wave = π - 0

= π

From the formula of the period,

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

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

b = 2

Therefore, a = 4 and b = 2.

Option (1) will be the answer.