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

Answer:

Option (1)

Step-by-step explanation:

Equation of the given wave function,

f(x) = acos(bx)

Here, a = amplitude of the wave

Period of the wave = $\frac{2\pi }{B}$

From the graph attached,

Amplitude = $\frac{4-(-4)}{2}$

                 = $\frac{4+4}{2}$

                 = 4

Period of the wave = π - 0

                                = π

From the formula of the period,

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

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

b = 2

Therefore, a = 4 and b = 2.

Option (1) will be the answer.