Question

Which of the following trigonometric functions matches the described characteristics: a cosine curve with a period of 4π, an amplitude of 3, a right phase shift of π/3, and a vertical translation up 4 units?

A) y = 3 cos (x - π / 3) + 4
B) y = 3 cos (x - π / 6) + 4
C) y = 3 cos (2x - π / 3) + 4
D) y = 3 cos (2x + π / 3) + 4

Answer 1

The trigonometric function that matches the given characteristics is y = 3 cos (x - π/3) + 4 (option A).

Step-by-step explanation:

The trigonometric function that matches the described characteristics is y = 3 cos (x - π / 3) + 4 (option A).

To determine the correct function, we need to consider each characteristic:

1. The period of the cosine curve is given by 2π / |b|, where b is the coefficient of x. In this case, the period is 4π. Therefore, the coefficient of x should be 1/4.
2. The amplitude of the cosine curve is the absolute value of the coefficient of the cosine term. In this case, the amplitude is 3.
3. The right phase shift is represented by a positive value in parentheses in the equation. In this case, the right phase shift is π / 3.
4. The vertical translation up represents a shift in the position of the graph vertically. In this case, the graph is shifted up by 4 units.

Therefore, the correct equation is y = 3 cos (x - π / 3) + 4 (option A).