Lesson 3-3

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3-3- Graphs of Tangent, Cotangent, Secant, and Cosecant Functions

Main Concepts

3-3 objectives is to allow us to visualize the graphs of Tangent, Cotangent, Secant, and cosecant functions, and show the behaviors and details of the functions.

1- Tangent Graph

• Tan (X)=Sin(X)/Cos(X) values of the Sin(X) is the values of X-intercept. So, If Sin(X)=0 then the Tan(X) is 0. Cos(X) is the value of Y-intercept. If Cos(x)=0, then Tan(X)=undefined. If Sin and Cos are equal then Tan is 1 and if they are opposites then Tan is -1.

• Vertical Asymptote, every time the function is undefined

• Period length is 180 degrees.
  

Cotangent Graph

• Cot(X)=Cos(X)/Sin(X), all the details of Tan(X) is oppisite for Cot(X).
  

• There is an Asymptote, everytime the sin(X) is 0 because it is undefined.
  

• Period length is 180 degrees.

2- Secant Graph

• Sec(X)=1/Cos(X)
  
  
• The reciprocal of the Cosine function is the Secant function. When the Cos(X)=0, then the secant is undefined and it has an Asymptote.

• When Cosine value is larger, then the Secant value is smaller, and vica versa. The Period length is 360 degrees. Origin is at 1.
  

3- Cosecant Graph

• Csc(X)=1/Sin(X)

• Sin and cosecant are reciprocals, and as the cosecant gets bigger, the Sin gets smaller, and vice versa.

• Asymptote occurs as the Sin is 0 and the Cosecant becomes undefinded. The Period length is 360 degrees. Origin is at 1.

Example Problem

Problem- Graph the function of Sin(X). Use the fact that Csc(X)=1/Sin(x) to sketch the graph of the cosecant fuction. Describe the function and the asymptote.

Solution- 1st-Sketch of the Sin(X) graph

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2nd- sketch the Csc(x) graph

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1. Where the sine function is 0, the cosecant function is undefined and has a vertical asymptote.When the sine function equals 1 and -1, so does the coseacant function. As the sine function get smaller, the coseacant function gets bigger.

Additional Resources

http://home.alltel.net/okrebs/page74.html is an internet site that will help you clear any extra questions up about these concepts.

Claire your up next;Have fun with your first blog and Good luck

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