Tangent Function Concepts and Properties

The video tutorial covers the unique characteristics of the tangent graph, including its vertical asymptotes and period. It explains how the tangent graph differs from sine and cosine graphs, particularly in terms of its period and amplitude. The tutorial also discusses the skeleton equation and how to determine the amplitude and midline. Finally, it touches on the relevance of the tangent graph in exams and provides practice questions for better 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.

At which points is the tangent function not defined on the unit circle?

• 0 and π

• π/2 and 3π/2

• π/4 and 3π/4

• π/6 and 5π/6

What is the relationship between the tangent function and the unit circle?

• Tangent is the ratio of sine to cosine.

• Tangent is the ratio of cosine to sine.

• Tangent is the sum of sine and cosine.

• Tangent is the difference between sine and cosine.

What do vertical asymptotes on the tangent graph represent?

• Points where tangent is minimum.

• Points where tangent is maximum.

• Points where tangent is undefined.

• Points where tangent is zero.

What happens to the tangent graph as it approaches a vertical asymptote?

• It becomes a straight line.

• It approaches infinity.

• It becomes undefined.

• It approaches zero.

What is the period of the parent tangent graph?

• π

• 3π

• 2π

• π/2

How do you determine the period of a tangent function?

• By finding the distance between two vertical asymptotes.

• By finding the distance between two x-intercepts.

• By finding the distance between two y-intercepts.

• By finding the distance between two maxima.

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

• The maximum value of the function.

• The average value around which the function oscillates.

• The minimum value of the function.

• The x-intercept of the function.

What is the role of the phase shift in the skeleton equation of tangent functions?

• It determines the horizontal shift of the graph.

• It determines the vertical shift of the graph.

• It determines the amplitude of the graph.

• It determines the period of the graph.

How does the tangent graph change as it crosses the midline?

• It changes from concave up to concave down.

• It changes from concave down to concave up.

• It becomes a straight line.

• It becomes undefined.