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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