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53 Cards in this Set

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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)
-√(1-cos^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^2-2bcCos<A
Sin(A+B)
SinACosB+SinBCosA
Sin(A-B)
SinACosB-SinBCosA
Cos(A+B)
CosACosB-SinASinB
Cos(A-B)
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
(x-h)^2+(y-K)^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(x-c) 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^2-4(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)^2-1
1-2(sinx)^2