Understanding the Tangent Function

This video tutorial covers the unique characteristics of the tangent graph, including its undefined points and vertical asymptotes. It explains how the tangent graph differs from sine and cosine graphs, particularly in its period and amplitude. The tutorial also provides guidance on how to analyze the tangent graph and its components, such as the midline and phase shift. Although the tangent graph may not be heavily featured in exams, the video includes practice questions to reinforce understanding.

Why is the tangent graph considered unique compared to sine and cosine graphs?

• It is a linear function.

• It has vertical asymptotes.

• It is defined at all points on the unit circle.

• It has a period of 2π.

How are tangent solutions derived from the unit circle?

• By using sine over cosine.

• By using cosine over sine.

• By using sine over tangent.

• By using tangent over sine.

At which points is the tangent function not defined?

• π/3 and 2π/3

• π/4 and 3π/4

• π/2 and 3π/2

• 0 and π

What is the period of the parent tangent graph?

• π

• 2π

• π/2

• 3π

What does the midline represent in the skeleton equation of tangent functions?

• The horizontal shift of the function.

• The average value of the function.

• The maximum value of the function.

• The vertical shift of the function.

How is the phase shift represented in the tangent function's skeleton equation?

• As the vertical shift.

• As the horizontal shift.

• As the coefficient of the tangent function.

• As the period of the function.

What is the role of 'B' in the tangent function's skeleton equation?

• It determines the period.

• It determines the phase shift.

• It determines the amplitude.

• It determines the midline.

How is the amplitude of a tangent graph determined?

• By measuring the distance from the midline to the minimum point.

• By measuring the distance from the midline to the y-axis.

• By measuring the distance from the midline to the x-axis.

• By measuring the distance from the midline to the maximum point.

What is the amplitude of the tangent graph in the given example?

• 0

• 1

• Undefined

• 2

Why might the tangent graph not be a focus on the AP exam?

• It is similar to sine and cosine graphs.

• It was not included in past exams.

• It is not commonly used.

• It is too complex.