Understanding the Graph of the Tangent Function

The video tutorial explains how to graph the parent function of y = tangent(x). It begins with an introduction to the unit circle and the concept of tangent as the ratio of sine over cosine. The instructor calculates tangent values for specific angles, highlighting undefined values and asymptotes. The graphing process is demonstrated, showing how the tangent function behaves and approaches asymptotes. Finally, the video discusses the periodicity of the tangent function, emphasizing that one full cycle is the length of pi.

What is the purpose of using a unit circle in graphing the tangent function?

• To find the radius of the circle

• To determine the sine and cosine values

• To calculate the area of the circle

• To measure the circumference

How is the tangent function defined in terms of sine and cosine?

• Tangent is the sum of sine and cosine

• Tangent is the difference between sine and cosine

• Tangent is the product of sine and cosine

• Tangent is the ratio of sine over cosine

What is the tangent value at 0 radians?

• 1

• 0

• -1

• Undefined

At which points is the tangent function undefined?

• At π and -π

• At π/4 and -π/4

• At 0 and π/4

• At π/2 and -π/2

What is the tangent value at π/4?

• 0

• 1

• Undefined

• -1

What do the undefined points in the tangent function graph represent?

• Minimum points

• Intercepts

• Asymptotes

• Maximum points

How does the tangent function behave as it approaches the asymptotes?

• It forms a straight line

• It increases or decreases without bound

• It oscillates

• It becomes constant

What happens to the tangent values as they approach zero?

• They approach zero

• They decrease

• They increase

• They become undefined

What is the period of the tangent function?

• π/2

• π

• 4π

• 2π

How does the tangent function repeat after one period?

• It mirrors itself

• It shifts vertically

• It repeats the same pattern

• It rotates 90 degrees