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53 Cards in this Set
 Front
 Back
derivatives

f(∆x+x) f(x)/∆x


arccsc

y=arcsin(1/x)


arcsec

y=arccos(1/x)


arccot

y=(π/2)arctanx


arcsin

domain= [1,1] range= [π/2, π/2]


arccos

domain= [1,1] range= [0,π]


arctan

domain= all real numbers range= [π/2, π/2]


sin

domain= [π/2,π/2] range=[1,1]


cos

domain= [0,π] range=[1,1]


tan

domain=[π/2, π/2] range= all real numbers


2^4

16


2^5

32


2^6

64


2^7

128


2^8

256


2^9

512


2^10

1024


2^11

2048


2^12

4096


2^13

8192


2^14

16384


2^15

32,768


2^16

65,536


2^17

131,072


2^18

262,144


2^19

524,288


2^20

1048576


sinw (in terms of cos)

√(1cos^2w)


secw (in terms of tan)

√(tan^2w +1)


Log(base z)y=b

z^b=y


sin(π/6)

1/2


sin(π/4)

√(2)/2


sin(π/3)

√(3)/2


cos(π/6)

√(3)/2


cos(π/4)

√(2)/2


cos(π/3)

1/2


law of sines

sin<A/a=sin<B/b=sin<C/c


law of cosines

a^2=b^2+c^22bcCos<A


Sin(A+B)

SinACosB+SinBCosA


Sin(AB)

SinACosBSinBCosA


Cos(A+B)

CosACosBSinASinB


Cos(AB)

CosACosB+SinASinB


Exponential growth formula

P(t)=P(initial)e^kt
t=time p(O/initial)=population initially k=constant 

exponential decay formula

1/2P(o)=P(o)e^kt


equation of a circle

(xh)^2+(yK)^2=r^2


vertical line test

equation is a function only if every verticle line intersects with the equation at the most once


horizontal shifts of graphs

f(xc) y=f(x) shifted to the right c units
f(x+c) y=f(x) shifted to the left c units 

vertical shifts of graphs

y=f(x)+c y= f(x)shifted upward c units
y=f(x)c y=f(x) shifted donward c units 

quadratic equation

b+/√(b^24(a)(c))/2a


pythagorean identty

(sint)^2+(cost)^2=1


y=Asin(Bx+C)
y=Acos(Bx+C) 
absolute value A=amplitude
period is 2π/B horizontally shifted by absolute value C/B> shift is left when C/B >O shift is right when C/B< O 

sine2x

2sinxcosx


cos2x

(cosx)^2(sinx)^2
2(cosx)^21 12(sinx)^2 