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TRIG – Chapter 5 – Identities

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TRIG – Chapter 5 – Identities Powered By Docstoc
					                                  MAC 1114 - TRIG –5.2a



A. Complete the right side using the indicated identity
   I. Reciprocal Identities

    sin  =            cos  =                       sec  =


    csc  =            tan  =                       cot  =



  II. Quotient Identities

    tan  =                                cot  =


 III. Pythagorean Identities and the alternate versions of each

   cos2  + sin2  =


   1 + tan2  =


    cot2  + 1 =


 IV. Co-function Identities

    sin  =                      cos  =                          tan  =



  V. Negative Angle Identities

     sin ( -  ) =               cos ( -  ) =                    tan ( -  ) =
   B. Match the expression on the left with an equivalent expression on the right.
   (Taken from page 187 problems 29 – 33 in the text)

      Column I                           Column II

           cos x
     1.                                 (a) sin2 x + cos2 x
           sin x

     2. tan x                           (b) cot x

     3. cos ( - x )                     (c) sec2 x

                                              sin x
     4. tan2 x + 1                      (d)
                                              cos x

    5. 1                                (e) cos x


C. Simplify the left side using properties of algebra (if possible).
   6. sin x + sin x =                            7. sin x – sin x =




                                                      sin x
   8. sin x  sin x =                            9.         =
                                                      sin x




   10. sin x + sin y =                           11. sin x ( 1 + sin x ) =




          sin 2 x
   12.            =
           sin x
D. Use properties of Algebra and substitutions based on Trig Identities to perform
the indicated operations and simplify your answers. Your simplified answers
should not contain parentheses or fractions.
           cos 2 x sin 2 x                                 cos x sin x
      13.                                            14.       
             3       3                                     sin x cos x


                  1     sin x                                             1       sin x
       15.                                                     16.            
                sin x 1  cos x                                       1  cos x 1  cos x


       17.   ( 1 + tan x )2 – 2 tan x


Simplify each expression to a constant, a single trig function or a power of a function.
           sin 2 x
    18.        2
                                                           19. cot x tan2 x
           cos x


                                                                        1
     20.     cot x sin x                                      21..             cot x tan x
                                                                      tan 2 x



E. Match the expression on the left with an equivalent expression on the right.
    Column I                               Column II

                                                    sin 2 x
 22. -tan x cos x                             (a)
                                                    cos 2 x

                                                      1
 23. sec2 x – 1                               (b)
                                                    sec2 x

        sec x
 24.                                          (c) sin ( - x )
        csc x

 25. 1 + sin2 x                               (d) csc2 x – cot2 x + sin2 x


26. cos2 x                                    (e) tan x

				
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Lingjuan Ma Lingjuan Ma MS
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