4f Characteristics of Cotangent (Parts of the Cotangent Graph)

The video tutorial covers the cotangent function, explaining its properties, graph, and behavior. It compares cotangent with tangent, highlighting differences in asymptotes and intercepts. The tutorial also discusses transformations and reciprocal relationships in trigonometric functions, using sine, cosine, cosecant, and secant as examples. The video concludes with a brief introduction to examples for further exploration.

What is the domain of the cotangent function?

• All real numbers except multiples of π

• All real numbers except multiples of π/2

• All real numbers except multiples of 2π

• All real numbers

Where are the asymptotes of the cotangent function located?

• At x = 2πn

• At x = πn

• At x = π/4 + πn

• At x = π/2 + πn

What is the x-intercept of the cotangent function?

• At x = 0

• At x = π/2

• At x = 3π/2

• At x = π

How does the cotangent function compare to the tangent function?

• It is a compressed version of the tangent function

• It is a mirrored image of the tangent function

• It is a horizontal shift of the tangent function

• It is a vertical stretch of the tangent function

What happens to the sine graph when it is vertically stretched?

• It compresses vertically

• It shifts horizontally

• It becomes a cosine graph

• It mirrors the cosecant graph

How does a vertical shift affect the secant graph?

• It moves the graph up or down

• It compresses the graph

• It stretches the graph

• It mirrors the graph

What remains consistent between transformations of tangent and cotangent functions?

• Only the period changes

• Phase shift, vertical translation, and period change

• Only the phase shift changes

• Only the vertical translation changes