Tangent Functions and Their Properties

The video tutorial covers the tangent function, explaining its relationship with the unit circle and how to calculate tangent values using angles. It discusses the properties of the tangent function, including its period and asymptotes, and demonstrates how to graph tangent functions. The tutorial emphasizes the importance of practice in mastering these concepts.

What is the tangent of an angle derived from?

• The radius of the unit circle

• The coordinates of a point on a line tangent to the unit circle

• The diameter of the unit circle

• The circumference of the unit circle

How do you find the tangent value of a 30-degree angle using the unit circle?

• Add the sine and cosine values

• Divide the sine value by the cosine value

• Subtract the cosine value from the sine value

• Multiply the sine and cosine values

What is the tangent of a 45-degree angle?

• 0

• 1

• √2

• √3

What is the parent tangent function?

• y = a * tan(Bθ)

• y = tan(θ)

• y = a * sin(Bθ)

• y = cos(θ)

What is the period of the standard tangent function?

• π/2

• 2π

• 2π/3

• π

How do you find the tangent value of negative π/3 using a graph?

• By finding the intersection with the tangent function

• By finding the intersection with the sine function

• By finding the intersection with the y-axis

• By finding the intersection with the x-axis

What is the period of the function y = tan(2θ)?

• π/4

• 2π

• π

• π/2

Where do vertical asymptotes occur in a tangent function?

• At the maximum points

• At the minimum points

• At the end of each cycle

• At the origin

What is the period of the function y = tan(-3/2πθ)?

• 2π

• 2π²/3

• π/3

• π²/3

What is the interval of one cycle for the function y = tan(-3/2πθ)?

• π²/3 to -π²/3

• -π²/3 to π²/3

• 0 to π

• -π to π