Wednesday, November 11, 2009

Graphs of Reciprocal Trigonometric Functions

Today in class we learned how to interpret and graph reciprocal trigonometic functions. 

Essentially, reciprocal trigonometric functions are related to the three primary trigonometric functions (sin, cos, tan). Since csc, sec, and cot graphs are just the reciprocals of sin, cos, and tan, respectively, the values of recirpocal trigonometic functions can be determined by simply flipping the denominator and numerator. Another key feature of reciprocal trignometic functions are the fact that they all have vertical asymptotes.

Example: graphing csc graph (above)

- Notice how there is an asymptote in everything 0+ k π value. This occurs because in a sin graph, those particular values would be 0, so therefore as the reciprocal of the sin graph, the values would be from 0/1 to 1/0. This will result it the value becoming undefined, hence becoming the vertical asymptotes. 

- There is restrictions for the y values as it has to be lower than 1 but bigger than -1. 

- There is no maximum or minimum value for y = cscx because the function approaches negative and positive infinity

- Since there is no maximum or minimum value for the function, there will be no amplitude. 

Overview of Reciprocal Trigonometic Functions

- The values of these types of functions (csc, sec, cot) can be determined by using the reciprocals of their counterparts. This is logically since they are technically just recirprocals of each other. 

Cot = 1/tanx  ;      Sec = 1/cosx       ;      Csc = 1/sinx 

- There will always be a vertical asymptote for every graph. 

- There will be no maximum or minimum values since it approaches positive and negative infinity 

- there will be no amptitudes 

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