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 "RealWorld" Page Everything for Calculus
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1. $f'(x) = \cos x + \sin x$

3. $g'(x) = (\cos x)(\tan x) + (\sin x)(\sec^2x)$

5. $h'(x) = -2\cosec x \cotan x - \sec x \tan x + 3$

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

9. $s'(x) = (2x-1)\tan x + (x^2-x+1)\sec^2x$

11. $t'(x) = \frac{-(\cosec^2x)(\sec x)(\tan x) - \sec x}{(1 + \sec x)^2}$

13. $k'(x) = -2\cos x \sin x$

15. $j'(x) = 2\sec^2x \tan x$

17. $u'(x) = -(2x - 1)\sin(x^2 - x)$

19. $v'(x) = (2.2x^{1.2}+1.2)\sec(x^{2.2}+1.2x-1)\tan(x^{2.2}+1.2x-1)$

21. $w'(x) = \sec x \tan x \tan(x^2 - 1) + 2x \sec x\ \sec^2(x^2 - 1)$

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

25. $z'(x) = \sec x$

27. $z'(x) = \sec x$

31.$e^{-2x}[-2\sin(3x) + 3\cos(3x)]$

33. $1.5[\sin(3x)]^{-0.5}\cos(3x)$

35. $\sec(x^3/x^2-1) \tan(x^3/x^2-1) (x^4-3x^2) / (x^2-1)^2$

37. $(1/x)\cotan(2x-1) - 2\ln \|x\| \cosec^2(2x-1)$

39. $c'(t) = (3.5)(2\pi)\cos[2\pi(t-0.75)];\ \ c'(0.75) \approx 21.99$ per year$\approx 42$ per week

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

43. $c'(t) = 1.035^t[\ln \|1.035\|(0.8\sin(2\pit) + 10.2) + 1.6\pi \cos(2\pit)];\ \ c'(1) = 1.035[10.2\ln \|1.035\|+ 1.6\pi] \approx 5.5656$ 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 "RealWorld" Page Everything for Calculus
Return to Exercises

We would welcome comments and suggestions for improving this resource. Mail us at:
Stefan Waner (matszw@hofstra.edu) Steven R. Costenoble (matsrc@hofstra.edu)
Last Updated: September, 1996
Copyright © 1996 StefanWaner and Steven R. Costenoble