Derivatives of Trigonometric Functions
          MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.
          Find the derivative.
                   1) y =  8  + 6 sec x                                                                                               1)
                          x
                               ′      8          2                                      ′      8
                         A) y  = -  2 + 6 tan x                                    B) y  = -  2 - 6 csc x
                                     x                                                        x
                         C)y′ =  8  - 6 sec x tan x                               D) y′  = -  8  + 6 sec x tan x
                                     2                                                          2
                                   x                                                          x
                   2) y =    2   +    1                                                                                               2)
                          sin x     cot x
                               ′                2                                       ′                        2
                         A) y  = 2 cos x - csc  x                                  B) y  = - 2 csc x cot x + sec  x
                               ′                      2                                 ′                      2
                         C)y  = 2 csc x cot x - csc  x                            D) y  = 2 csc x cot x - sec  x
                          7
                   3) s = t  - csc t + 2                                                                                              3)
                             ds      6                                                ds      6       2
                         A) dt  = 7t  + csc t cot t                                B) dt  = 7t  + cot t
                             ds      6                                                ds     6      2
                         C) dt  = 7t  - csc t cot t                               D) dt  = t  - cot t + 2
                               3
                   4) r = 9 - θ  cos θ                                                                                                4)
                              dr       2          3                                   dr          2           3
                         A) dθ = 3θ  sin θ - θ  cos θ                              B) dθ = - 3θ  cos θ + θ  sin θ
                              dr       2           3                                  dr        2
                         C) dθ = 3θ  cos θ - θ  sin θ                             D) dθ = 3θ  sin θ
          Solve the problem.
                   5) Find the tangent to y = cos x at x =  π .                                                                       5)
                                                              2
                         A) y = 1                     B) y = x +  π               C)y = - x -  π              D) y = - x +  π
                                                                  2                             2                            2
                   6) Find the tangent to y = 2 - sin x at x = π.                                                                     6)
                         A) y = - x + π - 2           B) y = x - π + 2            C)y = x - 2                 D) y = - x + 2
                   7) Find the tangent to y = cot x at x =  π .                                                                       7)
                                                              4
                         A) y = 2x + 1                                             B) y = 2x -  π  + 1
                                                                                                2
                         C)y = -2x +  π + 1                                       D) y = -2x +  π
                                         2                                                       2
                                                                              1
    Answer Key
    Testname: DERIVATIVES OF TRIGONOMETRIC FUNCTIONS
      1) D
      2) B
      3) A
      4) B
      5) D
      6) B
      7) C
                               2