Understanding the Graph of the Cotangent Function

This lesson demonstrates how to graph y = cotangent x over a specified interval using Desmos. It explains the relationship between cotangent and tangent functions, highlighting where cotangent is undefined and where it equals zero. The video guides viewers through setting up the graphing tool, identifying key points, and sketching the graph by hand. It emphasizes the differences in behavior between cotangent and tangent graphs, particularly in terms of asymptotes and function values.

What is the relationship between the cotangent and tangent functions?

• Cotangent is the reciprocal of tangent.

• Cotangent is the square of tangent.

• Cotangent is the derivative of tangent.

• Cotangent is the inverse of tangent.

Why does the cotangent function have vertical asymptotes?

• Because cotangent is zero where tangent is undefined.

• Because cotangent is always positive.

• Because cotangent is undefined where tangent is zero.

• Because cotangent is always negative.

What is the first step in graphing the cotangent function using Desmos?

• Set the calculator to radian mode.

• Adjust the y-axis settings.

• Set the calculator to degree mode.

• Change the color of the graph.

What happens to the cotangent function where the tangent function has a vertical asymptote?

• Cotangent is undefined.

• Cotangent equals one.

• Cotangent equals negative one.

• Cotangent equals zero.

At which points does the cotangent function intersect the x-axis?

• At points where tangent equals negative one.

• At points where tangent equals one.

• At points where tangent is undefined.

• At points where tangent is zero.

What is the value of the tangent function at 45 degrees?

• Zero

• Undefined

• One

• Negative one

Which of the following points is on both the tangent and cotangent graphs?

• Tangent 180 degrees

• Tangent 270 degrees

• Tangent 45 degrees

• Tangent 90 degrees

How does each piece of the cotangent graph behave from left to right?

• It oscillates.

• It increases.

• It decreases.

• It remains constant.

What is a key difference between the graphs of tangent and cotangent?

• Both graphs increase.

• Tangent graph increases, cotangent graph decreases.

• Tangent graph decreases, cotangent graph increases.

• Both graphs decrease.

What is the significance of the points where tangent equals negative one for the cotangent graph?

• Cotangent is undefined.

• Cotangent equals zero.

• Cotangent equals negative one.

• Cotangent equals one.