Question

The function f(x) = sin(x) is the result of the application of transformations on the original function F(x) = cos(x) . Which of the following options correctly describes the transformations applied to F(x) ?

A. A vertical shift of -1 unit
B. A vertical shift of 1 unit
C. A phase shift of π/2 radians
D. A phase shift of π radians

Answer 1

The function f(x) = sin(x) is the result of applying two transformations to the original function F(x) = cos(x): a vertical shift of 1 unit upwards and a phase shift of π/2 radians to the right.

Step-by-step explanation:

The function f(x) = sin(x) is the result of applying two transformations to the original function F(x) = cos(x). First, there is a vertical shift of 1 unit upwards, which moves the entire graph of the function vertically. Second, there is a phase shift of π/2 radians to the right, which shifts the graph horizontally.

So, the correct option is C. A phase shift of π/2 radians.