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87 Cards in this Set
- Front
- Back
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[sin u] '
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(cos u)u'
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[cos u] '
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-(sin u)u'
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[-sin u] '
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(-cos u)u'
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[-cos u] '
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(sin u)u'
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[tan u] '
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(sec u)^2 u'
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[cot u] '
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-(csc u)^2 u'
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[sec u] '
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(sec u)(tan u)u'
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[csc u] '
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-(csc u)(cot u)u'
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[arcsin u] '
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u' / √(1-u^2)
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[arccos u] '
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-(u' / √(1-u^2))
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[arctan u] '
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u' / (1+u^2)
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[arccot u] '
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-(u' / (1+u^2))
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[arcsec u] '
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u' / ( IuI √(1-u^2) )
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[arccsc u] '
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-[u' / ( IuI √(1-u^2) )]
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[u/v] '
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(vu' - uv') / (v^2)
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∫ du/u
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ln IuI + C
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∫ e^u du
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e^u + C
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∫ sin u du
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-cos u + C
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∫ cos u du
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sin u + C
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∫ tan u du
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-ln lcos ul + C
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∫ cot u du
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ln lsin ul + C
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∫ sec u du
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ln lsec u + tan ul + C
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∫ csc u du
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-ln lcsc u + cot ul + C
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∫ (sec u)^2 du
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tan u + C
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∫ (csc u)^2 du
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-cot u + C
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∫ sec u tan u du
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sec u + C
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∫ csc u cot u du
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-csc u + C
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∫ du/(√(a^2 - u^2))
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arcsin (u/a) + C
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∫ du/(√(a^2 + u^2))
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(1/a) arctan (u/a) + C
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∫ du/(u √(u^2 - a^2))
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(1/a) arcsec (lul/a) + C
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area of a triangle using trig
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(1/2)absinc
where c is the angle between sides a and b |
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area of an ellipse
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πab
where a and b are the vertical and horizontal radii |
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circumference of an ellipse
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2π √([a^2 + b^2]/2)
where a and b are the vertical and horizontal radii |
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area of an equilateral triangle
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(√3)/4 s^2
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area of a parallelogram
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A = bh
where h is perpendicular to b |
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volume of a cone
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(πr^2h)/3
one third the area of the base times the height |
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area of a trapezoid
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average of the bases times height
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circumference of a circle
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πd or 2πr
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lateral surface area of a cone
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πr√(r^2 +h^2)
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lateral surface area of a cylinder
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2πrh or πdh
note importance in shells, where h = f(x) and r = x |
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area of a sector of a circle
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(θr^2)/2
θ in radians note that the area of a circle is πr^2 where θ = 2π |
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arc length of a sector of a circle
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s = θr
θ in radians |
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volume of a sphere
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(4/3)πr^3
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surface area of a sphere
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4πr^2
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(sin u)^2 + (cos u)^2 =
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1
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1 + (tan u)^2
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(sec u)^2
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1 + (cot u)^2
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(csc u)^2
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sin (π/2 - u)
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cos u
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cos (π/2 - u)
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sin u
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tan (π/2 - u)
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cot u
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sin (-u)
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-sin u
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cos (-u)
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cos u
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tan (-u)
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-tan u
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sin (u+v)
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sin u cos v + cos u sin v
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sin (u-v)
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sin u cos v - cos u sin v
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cos (u+v)
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cos u cos v - sin u sin v
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cos (u-v)
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cos u cos v + sin u sin v
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sin (2u)
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2 sin u cos u
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cos (2u)
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(cos u)^2 - (sin u)^2
1 - 2(sin u)^2 2(cos u)^2 - 1 |
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2 sinu cosv
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sin (u+v) + sin (u-v)
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2 cos u cos v
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cos (u+v) + cos (u-v)
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2 cos u sin v
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sin (u+v) - sin (u-v)
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2 sin u sin v
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cos (u-v) - cos (u+v)
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sin 0
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0
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cos 0
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1
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tan 0
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0
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sin 30°
sin (π/6) |
1/2
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cos 30°
cos (π/6) |
√(3)/2
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tan 30°
tan (π/6) |
√(3)/3
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sin 45°
sin (π/4) |
√(2)/2
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cos 45°
cos (π/4) |
√(2)/2
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tan 45°
tan (π/4) |
1
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sin 60°
sin (π/3) |
√(3)/2
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cos 60°
cos (π/3) |
1/2
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tan 60°
tan (π/3) |
√(3)
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sin 90°
sin π/2 |
1
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cos 90°
cos π/2 |
0
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sin 180°
sin π |
0
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cos 180°
cos π |
-1
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sin 270°
sin 3π/2 |
-1
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cos 270°
cos 3π/2 |
0
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sin 360°
sin 2π |
0
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cos 360°
cos 2π |
1
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tan 360°
tan 2π |
0
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tan 180°
tan π/2 |
0
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tan 270°
tan 3π/2 |
--
cannot divide by 0 |
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tan 90°
tan π/2 |
--
cannot divide by 0 |
