Understanding the Tangent Function

The video tutorial illustrates the graph of the tangent function using the unit circle. It explains how the tangent of an angle is the ratio of the y-coordinate to the x-coordinate on the unit circle. The video demonstrates how the tangent function behaves as the angle increases, highlighting that it becomes undefined when the x-coordinate is zero. It also discusses the periodicity of the tangent function, which is different from sine and cosine, and shows the presence of vertical asymptotes. The tutorial concludes with a full view of the tangent graph from -2π to 2π radians, emphasizing the range and domain of the function.

What is the primary goal of illustrating the tangent function using the unit circle?

• To demonstrate the periodicity of trigonometric functions

• To show the relationship between sine and cosine

• To visualize the tangent function's graph

• To explain the concept of radians

As the angle approaches 90 degrees, what happens to the tangent function?

• It approaches zero

• It becomes undefined

• It decreases

• It remains constant

At what angle is the tangent function first undefined?

• 0 degrees

• 45 degrees

• 90 degrees

• 180 degrees

What is the period of the tangent function?

• 270 degrees

• 90 degrees

• 180 degrees

• 360 degrees

How does the tangent function compare to sine and cosine in terms of periodicity?

• It has the same period as sine and cosine

• It has a shorter period than sine and cosine

• It has a longer period than sine and cosine

• It is not periodic

What happens to the tangent function when the angle is negative?

• It mirrors the sine function

• It becomes undefined

• It follows a similar pattern as positive angles

• It becomes zero

What are vertical asymptotes in the context of the tangent function?

• Points where the function is undefined

• Points where the function is maximum

• Points where the function is minimum

• Points where the function is zero

What is the range of the tangent function?

• Negative infinity to positive infinity

• 0 to 1

• -1 to 1

• 0 to infinity

Which angles are excluded from the domain of the tangent function?

• Multiples of 45 degrees

• Multiples of 90 degrees

• Multiples of 60 degrees

• Multiples of 30 degrees

What is the domain of the tangent function?

• All angles except multiples of 90 degrees

• All angles except multiples of 180 degrees

• Only positive angles

• All real numbers