Understanding the Graph of Secant Function

This lesson explains how to graph the secant function y = secant x over the interval from -2π to 2π. It covers the relationship between the secant and cosine functions, highlighting that secant is the reciprocal of cosine. The video demonstrates setting up the graph using Desmos, noting the period and lack of amplitude due to vertical asymptotes where cosine equals zero. It also explores the connection between the graphs of cosine and secant, showing how to identify key points and asymptotes. The lesson concludes with tips on finding additional points using the reciprocal relationship.

What is the relationship between the secant and cosine functions?

• Secant is the derivative of cosine.

• Secant is the integral of cosine.

• Secant is the reciprocal of cosine.

• Secant is the square of cosine.

Where is the secant function undefined?

• Where cosine is 2.

• Where cosine is -1.

• Where cosine is 1.

• Where cosine is 0.

What is the period of the secant function?

• π/2 radians

• 2π radians

• 4π radians

• π radians

Why does the secant function have no amplitude?

• Because it is a constant function.

• Because it oscillates between fixed values.

• Because it extends infinitely in both directions.

• Because it is a linear function.

At which points does the secant function have vertical asymptotes?

• Where cosine equals -1.

• Where cosine equals 2.

• Where cosine equals 0.

• Where cosine equals 1.

What happens to the secant function at points where the cosine function equals 1?

• Secant is undefined.

• Secant equals 1.

• Secant equals 0.

• Secant equals -1.

How does the secant function behave near its vertical asymptotes?

• It approaches zero.

• It remains constant.

• It approaches infinity.

• It oscillates.

What is the secant function value at x = π/3 if the cosine value is 1/2?

• 0

• 1/2

• 2

• 1

What is the secant function value at x = -π/3 if the cosine value is 1/2?

• 1

• 1/2

• 2

• 0

How can additional points on the secant graph be found?

• By using the reciprocal relationship with the cosine function.

• By finding the derivative of the cosine function.

• By integrating the cosine function.

• By finding the square of the cosine function.