The Trigonometric Functions
by
Stefan Waner and Steven R. Costenoble

Answers to Exercises
for
Section 3: Derivatives of Trigonometric Functions

2. The Six Trigonometric Functions

3. Derivatives of Trigonometric Functions

4. Integrals of Trigonometric Functions

Trigonometric Functions Main Page

"Real World" Page

Return to Exercises

1. f'(x) = cos x + sin x

3. g'(x) = (cos x)(tan x) + (sin x)(sec²x)

5. h'(x) = 2cosecx cotan x sec x tan x + 3

7. r'(x) = cos x x sin x + 2x

9. s'(x) = (2x1)tan x + (x²x+1)sec²x

11. t'(x) =

(cosec2x)(sec x)(tan x) sec x (1 + sec x) 2

13. k'(x) = 2cos x sin x

15. j'(x) = 2sec²x tan x

17. u'(x) = (2x 1)sin(x² x)

19. v'(x) = (2.2x^1.2+1.2)sec(x^2.2+1.2x1)tan(x^2.2+1.2x1)

21. w'(x) = sec x tan x tan(x² 1) + 2x sec x sec²(x² 1)

23. y'(x) = e^x(sin(e^x) + cos x sin x)

25. z'(x) = sec x

27. z'(x) = sec x

31.e^2x[2sin(3x) + 3cos(3x)]

33. 1.5[sin(3x)] ^0.5cos(3x)

35. sec(x³/x²1) tan(x³/x²1) (x⁴3x²) / (x²1)²

37. (1/x)cotan(2x1) 2ln |x| cosec²(2x1)

39. c'(t) = (3.5)(2)cos[2(t0.75)]; c'(0.75) $21.99 per year 42¢ per week

41. (a) d(t) = 5cos(2t/13.5)+10 (b) d'(t) = (10/13.5)sin(2t/13.5); d'(7) 0.270. At noon, the tide was rising at a rate of 0.270 feet per hour.

43. c'(t) = 1.035^t[ln |1.035|(0.8sin(2t) + 10.2) + 1.6 cos(2t)];

c'(1) = 1.035[10.2ln |1.035|+ 1.6] $5.5656 per year, or $0.11 per week.

2. The Six Trigonometric Functions

3. Derivatives of Trigonometric Functions

4. Integrals of Trigonometric Functions

Trigonometric Functions Main Page

"Real World" Page

Return to Exercises

Stefan Waner (matszw@hofstra.edu)

Steven R. Costenoble (matsrc@hofstra.edu)

Last Updated: September, 1996 Copyright © 1996 StefanWaner and Steven R. Costenoble