Graphs of Trig Functions by 2bEj7R5

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									GRAPHS of Trig. Functions
GRAPHS of Trig. Functions

     We will primarily use the sin, cos, and tan function when graphing.
     However, the graphs of the other functions sec, csc, and cot will be
     covered.
GRAPHS of Trig. Functions

     Let’s begin with the cos x function. We can generate our values for
     the graph using our unit circle. Generally, you will graph from -2 pi
     to +2 pi.
GRAPHS of Trig. Functions

     Let’s begin with the cos x function. We can generate our values for
     the graph using our unit circle. Generally, you will graph from -2 pi
     to +2 pi.

                                                            f ( x)  cos x
                                     1

         2       3                        3   2
                            
                    2            2        2        2
                                     1
GRAPHS of Trig. Functions

      Let’s begin with the cos x function. We can generate our values for
      the graph using our unit circle. Generally, you will graph from -2 pi
      to +2 pi.

                                                                 f ( x)  cos x
                                           1

            2       3                          3   2
                               
                       2            2          2        2
                                         1
 cos 2   1
      7                  3 
 cos         0.7071  cos          0.7071
     4                      4 

     3                   
 cos    0            cos   0
      2                  2
      5                  
 cos         0.7071 cos        0.7071
     4                      4 
 cos    1         cos0   1
GRAPHS of Trig. Functions

      Let’s begin with the cos x function. We can generate our values for
      the graph using our unit circle. Generally, you will graph from -2 pi
      to +2 pi.

                                                                          f ( x)  cos x
                                           1

            2       3                               3    2
                               
                       2            2          2             2
                                         1
 cos 2   1
                             3                                         5   
      7             cos          0.7071    cos   0.7071        cos        0.7071
 cos         0.7071        4                     4                     4    
     4 
                                                                        3   
     3               cos   0                 cos   0             cos      0
 cos    0               2                        2                     2    
      2 
                                                   3                   7 
      5             cos        0.7071       cos       0.7071   cos      0.7071
 cos         0.7071       4                      4                    4 
     4 
                        cos0   1                cos   1           cos2   1
 cos    1
GRAPHS of Trig. Functions

      Let’s look at the sin function. Again, I generated values using the
      unit circle.



                                                                              f ( x)  sin x
                                             1

            2        3                                  3     2
                                  
                        2              2            2            2
                                            1
 cos 2   1
                                 3                                         5   
      7                 cos        0.7071        cos   0.7071      cos        0.7071
 cos         0.7071           4                      4                    4    
       4 
                                                                            3   
     3                   cos   0                  cos   0            cos      0
 cos    0                   2                         2                    2    
      2 
                                                        3                  7 
      5                 cos        0.7071       cos       0.7071   cos      0.7071
 cos         0.7071            4                       4                   4 
     4 
                            cos0   1                cos   1           cos2   1
 cos    1
GRAPHS of Trig. Functions

     The tangent function is different than sin and cosine. The tangent
     function has asymptotes that occur at certain values of pi because
     the function is undefined at that value.
GRAPHS of Trig. Functions

     The tangent function is different than sin and cosine. The tangent
     function has asymptotes that occur at certain values of pi because
     the function is undefined at that value.


                sin x
      tan x 
                cos x
GRAPHS of Trig. Functions

     The tangent function is different than sin and cosine. The tangent
     function has asymptotes that occur at certain values of pi because
     the function is undefined at that value.


                sin x
      tan x 
                cos x
                    
               sin  
                2
      tan  
          2  cos  
                    
                   2
GRAPHS of Trig. Functions

     The tangent function is different than sin and cosine. The tangent
     function has asymptotes that occur at certain values of pi because
     the function is undefined at that value.


                sin x
      tan x 
                cos x
                    
               sin  
                2
      tan  
          2  cos  
                    
                   2

           1
      tan            This is undefined…
         2 0

                                        
          Tangent is undefind for x        
                                        2
GRAPHS of Trig. Functions

     The tangent function is different than sin and cosine. The tangent
     function has asymptotes that occur at certain values of pi because
     the function is undefined at that value.


                sin x
      tan x 
                cos x
                    
               sin  
                2
      tan  
          2  cos  
                    
                   2

           1
      tan  
         2 0

                                   
     Tangent is undefind for x            3                   3
                                   2          2     2        2         2
GRAPHS of Trig. Functions

     The tangent function is different than sin and cosine. The tangent
     function has asymptotes that occur at certain values of pi because
     the function is undefined at that value.


                sin x
      tan x 
                cos x
                    
               sin  
                2
      tan  
          2  cos  
                    
                   2

           1
      tan  
         2 0

                                   
     Tangent is undefind for x            3                   3
                                   2          2     2        2         2
GRAPHS of Trig. Functions

     The cotangent function is similar to its cousin tangent as it too has
     asymptotes that occur at certain values of pi because the function is
     undefined at that value.


                cos x
      cot x 
                sin x
GRAPHS of Trig. Functions

     The cotangent function is similar to its tangent cousin. The cotangent
     function also has asymptotes that occur at certain values of pi
     because the function is undefined at that value.


                cos x
      cot x 
                sin x

                  cos 
      cot  
                  sin  


      cot  
                  1
                  0
GRAPHS of Trig. Functions

     The cotangent function is similar to its tangent cousin. The cotangent
     function also has asymptotes that occur at certain values of pi
     because the function is undefined at that value.


                cos x
      cot x 
                sin x

                   cos 
      cot  
                   sin  


       cot  
                   1
                   0


    Tangent is undefind for x    
                                         2                        2
GRAPHS of Trig. Functions

     The cotangent function is similar to its tangent cousin. The cotangent
     function also has asymptotes that occur at certain values of pi
     because the function is undefined at that value.


                cos x
      cot x 
                sin x

                   cos 
      cot  
                   sin  


       cot  
                   1
                   0


    Tangent is undefind for x    
                                         2                        2
GRAPHS of Trig. Functions



   I will leave the secant and cosecant graphs for you to research.
   Google them if you have to. Your assignment will be to find their
   graphs, determine the values where they are undefined, find the
   range of both functions, and at what intervals their asymptotes
   occurs.

								
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