Question

Write an equation for a function with the given characteristics. a cosine curve with a period of 8, an amplitude of 2, a right phase shift of /3, and a vertical translation up 3 units.

Answer 1

The equation for a cosine curve with the given characteristics would be:

f(x) = 2 * cos((2π/8) * (x - π/3)) + 3

Let's break down the components of the equation:
- The amplitude of 2 indicates that the cosine curve oscillates between -2 and 2.
- The period of 8 means that the curve completes one full cycle over an interval of length 8.
- The right phase shift of π/3 indicates that the curve is shifted horizontally to the right by π/3 units.
- The vertical translation up 3 units moves the entire curve vertically upward by 3 units.

By combining these characteristics, we form the equation f(x) = 2 * cos((2π/8) * (x - π/3)) + 3, which represents a cosine curve with the specified properties.