Question

Use the graph below to answer the question that follows: what trigonometric function represents the graph?

Options
f(x)=4sin(x-pi/2)

f(x)=-4sin(x-pi/2)

f(x)=4cos(x-pi/2)

f(x)=-4cos(x-pi/2)

Answer 1

Option (4)

Explanation:

From the graph attached,

Equation of the wave function is a cosine function.

Let the graphed function is, f(x) = -Acos(bx - ∅)

Amplitude of the given function,

A =
`(4-(-4))/(2)` = 4 units

Period =
`(2\pi )/(b)` = 2π

b =
`(2\pi )/(2\pi )` = 1

Given graph is starting from (0, 0).

Therefore, from the given graph, Phase shift of the cosine curve = ∅ =
`(\pi )/(2)`

Therefore, equation of the given cosine function will be,

f(x) = -4cos(x -
`(\pi )/(2)`)

Option (4) will be the answer.