Tangent and Cotangent Functions

This video tutorial by Mr. Backer covers lesson 4.6 on graphing tangent and cotangent functions. It begins with an introduction to the objectives, which include sketching graphs of tangent functions and understanding their characteristics. The video provides step-by-step instructions on graphing tangent functions, highlighting key characteristics such as period and domain issues. Several examples are given to illustrate the graphing process. The tutorial also introduces cotangent functions, explaining their similarities and differences with tangent functions. The video concludes with a summary and a call to action for viewers to complete a Google form.

What are the two main objectives of this lesson?

• Sketching graphs of sine and cosine functions

• Sketching graphs of tangent and cotangent functions

• Solving trigonometric equations

• Understanding the unit circle

When graphing a tangent function, what do you do when you encounter an undefined value?

• Ignore it

• Plot it as zero

• Mark it as a vertical asymptote

• Use it as an intercept

What is the period of a tangent function?

• 2π

• 4π

• π

• π/2

How do you find the vertical asymptotes for a tangent function?

• Set the function equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set the function equal to infinity

In the example of y = tangent(x/4), what is the x-intercept?

• π/2

• 2π

• 0

• π

For the function y = tangent(2x), what is the distance between the vertical asymptotes?

• π

• π/2

• 2π

• π/4

In the function y = 1/4 tangent(x), what is the amplitude?

• 1

• Undefined

• 4

• 1/4

What is the main difference between tangent and cotangent functions?

• Amplitude

• Domain and asymptotes

• Range

• Period

In the example of y = cotangent(x/2), where is the x-intercept located?

• π

• 0

• π/2

• 2π