Understanding the Secant Function

This video tutorial explains how to graph the secant function using the reciprocal identity, where secant theta is the reciprocal of cosine theta. It covers identifying points on the secant graph by using known cosine values, understanding where vertical asymptotes occur when cosine is zero, and graphing the secant function in various intervals. The tutorial provides a step-by-step approach to sketching the secant graph by determining function values and asymptotes, ultimately leading to a complete graph of the secant function.

What is the reciprocal identity for the secant function?

• Secant theta is equal to one divided by cosine theta

• Secant theta is equal to one divided by sine theta

• Secant theta is equal to tangent theta

• Secant theta is equal to sine theta

What happens to the secant function when cosine theta equals zero?

• Secant theta is zero

• Secant theta is negative

• Secant theta is undefined

• Secant theta is one

At which point does the secant function have a vertical asymptote?

• Where cosine theta is one

• Where cosine theta is two

• Where cosine theta is negative one

• Where cosine theta is zero

In the interval from -π/2 to π/2, what is the secant value when cosine theta is 1/2?

• Secant theta is 2

• Secant theta is 4

• Secant theta is 1

• Secant theta is 3

What is the secant value when cosine theta is 1/4?

• Secant theta is 4

• Secant theta is 2

• Secant theta is 1

• Secant theta is 3

What is the reciprocal of cosine theta when it equals -1/2?

• -1

• -2

• -4

• -3

What is the secant value when cosine theta is -1/4?

• -4

• -3

• -2

• -1

How does the secant function behave between vertical asymptotes?

• It remains constant

• It oscillates

• It approaches infinity

• It approaches zero

What is the secant value when cosine theta is 1/2 in the final section?

• Secant theta is 3

• Secant theta is 4

• Secant theta is 2

• Secant theta is 1

What is the relationship between secant and cosine functions?

• Secant is the square of cosine

• Secant is the reciprocal of cosine

• Secant is the sum of cosine

• Secant is the difference of cosine