Question

Using complete sentences, explain the key features of the graph of the cosine function

Answer 1

The graph of the cosine function is attached below :

Explanation:

The key features of the graph of the cosine function are :

• Period = 2π

• x intercepts : x = π/2 + k·π , where k is an integer.

• y intercepts : y = 1

• maximum points : (2·k·π , 1) , where k is an integer.

• minimum points : (π + 2·k·π , -1) , where k is an integer.

• symmetry : since cos(-x) = cos (x) then cos (x) is an even function and its graph is symmetric with respect to the y axis.

• intervals of increase/decrease : over one period and from 0 to 2π, cos (x) is decreasing on (0 , π) increasing on (π , 2π).

Answer 2

Cosine function is an even sinusoidal function.

It crosses the y-axis at y = 1.

The range is [-1,+1], the amplitud is 1, the periodicity is 2π

Its roots (x-axis crossing points) are x = nπ - π/2, for n ∈ Z.