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

Answer:

Option (4)

Step-by-step 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 = $\frac{4-(-4)}{2}$ = 4 units

Period = $\frac{2\pi }{b}$ = 2π

b = $\frac{2\pi }{2\pi }$ = 1

Given graph is starting from (0, 0).

Therefore, from the given graph, Phase shift of the cosine curve = ∅ = $\frac{\pi }{2}$

Therefore, equation of the given cosine function will be,

f(x) = -4cos(x - $\frac{\pi }{2}$)

Option (4) will be the answer.