Objective- Evaluate trigonometric functions of any angle

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					Objective- Evaluate trigonometric functions of
                 any angle.

                          y
                 (x, y)
                              
                 r
                                  x

     r  x y2       2
        Six Trigonometric Functions

        y               y
                                        r
sin          (x, y)           csc  
        r                              y
                r
        x                                 r
cos                             sec  
        r                       x
                                          x

        y                               x
tan                           cot  
        x                               y
Evaluate the six trigonometric functions.

        y                     3               4
  (-4, 3)             sin         cos   
                              5               5
            
                                3         5
    r                 tan      csc  
                                4         3
                     x
r 5                            5             4
                      sec        cot   
                                4             3
If the terminal side of  lies on a axis,
      then  is a quadrantal angle.
                     y




                           0
                                  (r, 0)   x

                                  xr
                                  y0
If the terminal side of  lies on a axis,
      then  is a quadrantal angle.
                     y
                (0, r)
        x0
        yr
                           90
                                    x
If the terminal side of  lies on a axis,
      then  is a quadrantal angle.
                     y




        (-r, 0)            180
                                    x
            x  r
            y0
  If the terminal side of  lies on a axis,
         then  is a quadrantal angle.
                       y




                             270
                                      x
x0
y  r                      (0, -r)
Evaluate the six trigonometric functions of
                   90
              x  0, y  r

       y y                          x 0
sin     1                cos     0
       r y                          r r
       y y                          r r
tan     undefined        csc     1
       x 0                          y r
       r r                          x 0
sec   = = undefined        cot     0
       x 0                          y y
              Reference Angle
                        y

                            
                   '

                                  x




Reference Angle- is the acute angle  formed
                                      '

by the terminal side of  and the x-axis.
Find the reference  for each angle  .
                   '


1. 310                      2
                        4.
     360  310
     '
                              3
                                 2 
          50
          '
                           
                           '
                                     
                                  3 3
                             6
2. 170                5.
                                    5
      180 170
     '
                            6      
        10
        '                     
                                '

                         7  5      5
3. 200                6.
                                    4
      200 180
     '                          7 
                         2 
                            '
                                  
         20
        '
                                 4 4
1. Evaluate cos225
       225 180  45 Quadrant III
                                2
                             
2. Evaluate tan120            2

       180 120  60 Quadrant II

                11           3
3. Evaluate sin
                 6        Quadrant IV
                11            1
        2               
                 6    6         2