Derivatives of trig functions

Answer Key - Grade 12 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari differentiates f(x) = 4 cos x. What is f′(5π/6)?

   -2
2. 2.

   Bo differentiates f(x) = 6 cos x. What is f′(7π/6)?

   3
3. 3.

   Esme differentiates f(x) = 10 cos x. What is f′(11π/6)?

   5
4. 4.

   Jun differentiates f(x) = 14 cos x. What is f′(5π/6)?

   -7
5. 5.

   Luz differentiates f(x) = 5 sec x. Which is f′(x)?

   • f′(x) = −5 sec x tan x
   • f′(x) = 5 sec x tan x
   • f′(x) = 5 sec² x
   • f′(x) = −5 csc x cot x
6. 6.

   Milo differentiates f(x) = 2 cot x. Which is f′(x)?

   • f′(x) = 2 csc² x
   • f′(x) = −2 csc² x
   • f′(x) = −2 csc x cot x
   • f′(x) = 2 sec² x
7. 7.

   Noah differentiates f(x) = 4 csc x. Which is f′(x)?

   • f′(x) = 4 csc x cot x
   • f′(x) = −4 csc x cot x
   • f′(x) = −4 csc² x
   • f′(x) = 4 sec x tan x
8. 8.

   Pia finds the slope of f(x) = 10 sin x at x = 2π/3. What is f′(2π/3)?

   -5
9. 9.

   Ren finds the slope of f(x) = 8 sin x at x = 5π/3. What is f′(5π/3)?

   4
10. 10.

    Tala finds the slope of f(x) = 14 sin x at x = 4π/3. What is f′(4π/3)?

    -7