# calc

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1. √(a² + x²)
• x = a tan θ
• 1 + tan² θ = sec² θ, -½ π < θ < ½ π
2. √(a² - x²)
• x = a sin θ
• 1 - sin² θ = cos² θ, -½ π < θ < ½ π
3. √(x² - a²)
• x = a sec θ
• sec² θ - 1 = tan² θ, 0 < θ < 3π/2
4. sin 2x
2 sin x cos x
5. (1) cos 2x
cos² x - sin² x
6. (2) cos 2x
2 cos² x - 1
7. (3) cos 2x
1 - 2 sin² x
8. tan 2x
2 tan x / (1 - tan² x)
9. sin² x
(1 - cos 2x) / 2
10. cos² x
(1 + cos 2x) / 2
11. d/dx arcsin x
1 / √(1 - x²)
12. d/dx arccos x
-1 / √(1 - x²)
13. d/dx arctan x
1 / (1 + x²)
14. d/dx arccsc x
-1 / x√(x² - 1)
15. d/dx arcsec x
1 / x√(x² - 1)
16. d/dx arccot x
-1 / (1 + x²)
17. cos odd
factor cos x ; cos² x = 1 - sin² x ; u = sin x
18. sin odd
factor sin x ; sin² x = 1 - cos² x ; u = cos x
19. sin, cos odd
either
20. sin, cos even
half-angle identities ; sometimes use sin x cos x = sin 2x / 2
21. sec even
factor sec² x ; sec² x = 1 + tan² x ; u = tan x
22. tan odd
factor sec x tan x ; tan² x = sec² x - 1 ; u = sec x
23. tan even, sec odd
express all as sec
 Author: ixyl ID: 23164 Card Set: calc Updated: 2010-06-12 02:13:52 Tags: calc Folders: Description: calc Show Answers: