The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds can be modeled by the graph below. Which equation is represented in the graph below? On a coordinate plane, a curve crosses the y-axis at (0, negative 5). It increases to (1, 5) and then decreases to (2, negative 5). 5 cycles are shown.

The equation d = -5cos(πt) modeled the distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t.

We know the cosine equation for distance d:

d = acos(bt+c) + d

From the graph: a = -5, b = π

Assume the phase and vertical shift are zero.

c = 0 and d = 0

Plug all values in the function, the equation becomes:

d = -5cos(πt)

Thus, the equation d = -5cos(πt) modeled the distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds.

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