calc

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Author:
ixyl
ID:
23164
Filename:
calc
Updated:
2010-06-11 22:13:52
Tags:
calc
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Description:
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

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