Tangent Function Concepts and Properties

This video tutorial explores the properties of the tangent function, defined in terms of sine and cosine. It covers calculating tangent values at special points on the unit circle, graphing these values, and making observations about the function's behavior in different quadrants. The tutorial also discusses vertical asymptotes, periodicity, and the domain and range of the tangent function, providing a comprehensive understanding of its graph and properties.

What is the tangent of 0?

• 0

• 1

• Undefined

• Infinity

How is the tangent of π/4 calculated?

• Sine of π/4 plus cosine of π/4

• Sine of π/4 divided by cosine of π/4

• Cosine of π/4 divided by sine of π/4

• Sine of π/4 times cosine of π/4

In which quadrants is the tangent function positive?

• Quadrants III and IV

• Quadrants II and IV

• Quadrants I and II

• Quadrants I and III

What happens to the tangent function as it approaches π/2 from the left?

• It decreases without bound

• It increases without bound

• It remains constant

• It becomes zero

What is the period of the tangent function?

• π

• 2π

• π/2

• 4π

Where does the tangent function have vertical asymptotes?

• At T = π + kπ

• At T = 2π + kπ

• At T = π/2 + kπ

• At T = 3π/2 + kπ

What is the domain of the tangent function?

• All real numbers except T = 2π + kπ

• All real numbers except T = π + kπ

• All real numbers

• All real numbers except T = π/2 + kπ

What is the range of the tangent function?

• All real numbers

• Only negative numbers

• Only positive numbers

• Between -1 and 1

How does the tangent function behave on intervals where it is defined?

• It remains constant

• It oscillates

• It is always decreasing

• It is always increasing

What is the significance of the vertical asymptotes in the tangent function?

• They indicate where the function is zero

• They indicate the maximum value

• They indicate where the function is undefined

• They indicate the minimum value