baLivvycaitlyn
Answered

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

Verified Answer :

Edufirst

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.

Answer:

The graph of the cosine function is attached below :

Step-by-step 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).

View image throwdolbeau

Related Questions