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Quadratic formula

If a x 2 + b x + c = 0 , then x = b ± b 2 4 a c 2 a

Geometry
Triangle of base b and height h Area = 1 2 b h
Circle of radius r Circumference = 2 π r Area = π r 2
Sphere of radius r Surface area = 4 π r 2 Volume = 4 3 π r 3
Cylinder of radius r and height h Area of curved surface = 2 π r h Volume = π r 2 h

Trigonometry

Trigonometric Identities

  1. sin θ = 1 / csc θ
  2. cos θ = 1 / sec θ
  3. tan θ = 1 / cot θ
  4. sin ( 90 0 θ ) = cos θ
  5. cos ( 90 0 θ ) = sin θ
  6. tan ( 90 0 θ ) = cot θ
  7. sin 2 θ + cos 2 θ = 1
  8. sec 2 θ tan 2 θ = 1
  9. tan θ = sin θ / cos θ
  10. sin ( α ± β ) = sin α cos β ± cos α sin β
  11. cos ( α ± β ) = cos α cos β sin α sin β
  12. tan ( α ± β ) = tan α ± tan β 1 tan α tan β
  13. sin 2 θ = 2 sin θ cos θ
  14. cos 2 θ = cos 2 θ sin 2 θ = 2 cos 2 θ 1 = 1 2 sin 2 θ
  15. sin α + sin β = 2 sin 1 2 ( α + β ) cos 1 2 ( α β )
  16. cos α + cos β = 2 cos 1 2 ( α + β ) cos 1 2 ( α β )

Triangles

  1. Law of sines: a sin α = b sin β = c sin γ
  2. Law of cosines: c 2 = a 2 + b 2 2 a b cos γ
    Figure shows a triangle with three dissimilar sides labeled a, b and c. All three angles of the triangle are acute angles. The angle between b and c is alpha, the angle between a and c is beta and the angle between a and b is gamma.
  3. Pythagorean theorem: a 2 + b 2 = c 2
    Figure shows a right triangle. Its three sides are labeled a, b and c with c being the hypotenuse. The angle between a and c is labeled theta.

Series expansions

  1. Binomial theorem: ( a + b ) n = a n + n a n 1 b + n ( n 1 ) a n 2 b 2 2 ! + n ( n 1 ) ( n 2 ) a n 3 b 3 3 ! + ···
  2. ( 1 ± x ) n = 1 ± n x 1 ! + n ( n 1 ) x 2 2 ! ± ··· ( x 2 < 1 )
  3. ( 1 ± x ) n = 1 n x 1 ! + n ( n + 1 ) x 2 2 ! ··· ( x 2 < 1 )
  4. sin x = x x 3 3 ! + x 5 5 ! ···
  5. cos x = 1 x 2 2 ! + x 4 4 ! ···
  6. tan x = x + x 3 3 + 2 x 5 15 + ···
  7. e x = 1 + x + x 2 2 ! + ···
  8. ln ( 1 + x ) = x 1 2 x 2 + 1 3 x 3 ··· ( | x | < 1 )

Derivatives

  1. d d x [ a f ( x ) ] = a d d x f ( x )
  2. d d x [ f ( x ) + g ( x ) ] = d d x f ( x ) + d d x g ( x )
  3. d d x [ f ( x ) g ( x ) ] = f ( x ) d d x g ( x ) + g ( x ) d d x f ( x )
  4. d d x f ( u ) = [ d d u f ( u ) ] d u d x
  5. d d x x m = m x m 1
  6. d d x sin x = cos x
  7. d d x cos x = sin x
  8. d d x tan x = sec 2 x
  9. d d x cot x = csc 2 x
  10. d d x sec x = tan x sec x
  11. d d x csc x = cot x csc x
  12. d d x e x = e x
  13. d d x ln x = 1 x
  14. d d x sin −1 x = 1 1 x 2
  15. d d x cos −1 x = 1 1 x 2
  16. d d x tan −1 x = 1 1 + x 2

Integrals

  1. a f ( x ) d x = a f ( x ) d x
  2. [ f ( x ) + g ( x ) ] d x = f ( x ) d x + g ( x ) d x
  3. x m d x = x m + 1 m + 1 ( m 1 ) = ln x ( m = −1 )
  4. sin x d x = cos x
  5. cos x d x = sin x
  6. tan x d x = ln | sec x |
  7. sin 2 a x d x = x 2 sin 2 a x 4 a
  8. cos 2 a x d x = x 2 + sin 2 a x 4 a
  9. sin a x cos a x d x = cos 2 a x 4 a
  10. e a x d x = 1 a e a x
  11. x e a x d x = e a x a 2 ( a x 1 )
  12. ln a x d x = x ln a x x
  13. d x a 2 + x 2 = 1 a tan −1 x a
  14. d x a 2 x 2 = 1 2 a ln | x + a x a |
  15. d x a 2 + x 2 = sinh −1 x a
  16. d x a 2 x 2 = sin −1 x a
  17. a 2 + x 2 d x = x 2 a 2 + x 2 + a 2 2 sinh −1 x a
  18. a 2 x 2 d x = x 2 a 2 x 2 + a 2 2 sin −1 x a

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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