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87 Cards in this Set

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[sin u] '
(cos u)u'
[cos u] '
-(sin u)u'
[-sin u] '
(-cos u)u'
[-cos u] '
(sin u)u'
[tan u] '
(sec u)^2 u'
[cot u] '
-(csc u)^2 u'
[sec u] '
(sec u)(tan u)u'
[csc u] '
-(csc u)(cot u)u'
[arcsin u] '
u' / √(1-u^2)
[arccos u] '
-(u' / √(1-u^2))
[arctan u] '
u' / (1+u^2)
[arccot u] '
-(u' / (1+u^2))
[arcsec u] '
u' / ( IuI √(1-u^2) )
[arccsc u] '
-[u' / ( IuI √(1-u^2) )]
[u/v] '
(vu' - uv') / (v^2)
∫ du/u
ln IuI + C
∫ e^u du
e^u + C
∫ sin u du
-cos u + C
∫ cos u du
sin u + C
∫ tan u du
-ln lcos ul + C
∫ cot u du
ln lsin ul + C
∫ sec u du
ln lsec u + tan ul + C
∫ csc u du
-ln lcsc u + cot ul + C
∫ (sec u)^2 du
tan u + C
∫ (csc u)^2 du
-cot u + C
∫ sec u tan u du
sec u + C
∫ csc u cot u du
-csc u + C
∫ du/(√(a^2 - u^2))
arcsin (u/a) + C
∫ du/(√(a^2 + u^2))
(1/a) arctan (u/a) + C
∫ du/(u √(u^2 - a^2))
(1/a) arcsec (lul/a) + C
area of a triangle using trig
(1/2)absinc
where c is the angle between sides a and b
area of an ellipse
πab
where a and b are the vertical and horizontal radii
circumference of an ellipse
2π √([a^2 + b^2]/2)
where a and b are the vertical and horizontal radii
area of an equilateral triangle
(√3)/4 s^2
area of a parallelogram
A = bh
where h is perpendicular to b
volume of a cone
(πr^2h)/3

one third the area of the base times the height
area of a trapezoid
average of the bases times height
circumference of a circle
πd or 2πr
lateral surface area of a cone
πr√(r^2 +h^2)
lateral surface area of a cylinder
2πrh or πdh

note importance in shells, where h = f(x) and r = x
area of a sector of a circle
(θr^2)/2

θ in radians
note that the area of a circle is πr^2
where θ = 2π
arc length of a sector of a circle
s = θr

θ in radians
volume of a sphere
(4/3)πr^3
surface area of a sphere
4πr^2
(sin u)^2 + (cos u)^2 =
1
1 + (tan u)^2
(sec u)^2
1 + (cot u)^2
(csc u)^2
sin (π/2 - u)
cos u
cos (π/2 - u)
sin u
tan (π/2 - u)
cot u
sin (-u)
-sin u
cos (-u)
cos u
tan (-u)
-tan u
sin (u+v)
sin u cos v + cos u sin v
sin (u-v)
sin u cos v - cos u sin v
cos (u+v)
cos u cos v - sin u sin v
cos (u-v)
cos u cos v + sin u sin v
sin (2u)
2 sin u cos u
cos (2u)
(cos u)^2 - (sin u)^2

1 - 2(sin u)^2

2(cos u)^2 - 1
2 sinu cosv
sin (u+v) + sin (u-v)
2 cos u cos v
cos (u+v) + cos (u-v)
2 cos u sin v
sin (u+v) - sin (u-v)
2 sin u sin v
cos (u-v) - cos (u+v)
sin 0
0
cos 0
1
tan 0
0
sin 30°
sin (π/6)
1/2
cos 30°
cos (π/6)
√(3)/2
tan 30°
tan (π/6)
√(3)/3
sin 45°
sin (π/4)
√(2)/2
cos 45°
cos (π/4)
√(2)/2
tan 45°
tan (π/4)
1
sin 60°
sin (π/3)
√(3)/2
cos 60°
cos (π/3)
1/2
tan 60°
tan (π/3)
√(3)
sin 90°
sin π/2
1
cos 90°
cos π/2
0
sin 180°
sin π
0
cos 180°
cos π
-1
sin 270°
sin 3π/2
-1
cos 270°
cos 3π/2
0
sin 360°
sin 2π
0
cos 360°
cos 2π
1
tan 360°
tan 2π
0
tan 180°
tan π/2
0
tan 270°
tan 3π/2
--

cannot divide by 0
tan 90°
tan π/2
--

cannot divide by 0