Understanding the Graph of Cotangent Function

This lesson demonstrates how to graph y = cotangent x over the interval from -2π to 2π radians. It explains the relationship between cotangent and tangent functions, highlighting where cotangent is undefined and where it has vertical asymptotes. The video uses Desmos to visualize the graph and compares it to the tangent graph, showing key points where tangent equals 1 or -1. The lesson concludes by plotting these points and observing the behavior of the cotangent graph.

What is the relationship between cotangent and tangent functions?

• Cotangent is the reciprocal of sine.

• Cotangent is the same as tangent.

• Cotangent is the reciprocal of cosine.

• Cotangent is the reciprocal of tangent.

Where does the cotangent function have vertical asymptotes?

• Where cosine equals zero.

• Where tangent equals one.

• Where sine equals zero.

• Where tangent equals zero.

What happens to the cotangent graph at x = 0?

• It has a vertical asymptote.

• It is zero.

• It is one.

• It is undefined.

At which points is the cotangent function zero?

• Where cosine equals zero.

• Where sine equals zero.

• Where tangent has a vertical asymptote.

• Where tangent equals zero.

At which x-values does the cotangent graph intersect the x-axis?

• x = -3π/2, -π/2, π/2, 3π/2

• x = -π, 0, π

• x = -π/4, π/4

• x = -2π, -π, 0, π, 2π

What is the value of tangent at π/4?

• 0

• Undefined

• 1

• -1

What is the value of tangent at -π/4?

• 0

• Undefined

• 1

• -1

What is the value of tangent at 3π/4?

• 0

• -1

• Undefined

• 1

How does the cotangent graph behave between vertical asymptotes?

• It increases from left to right.

• It decreases from left to right.

• It remains constant.

• It oscillates.

What is the relationship between the direction of tangent and cotangent graphs?

• Both increase from left to right.

• Both decrease from left to right.

• Tangent increases while cotangent decreases from left to right.

• Tangent decreases while cotangent increases from left to right.