Math Final Card

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1 degree=pi/180

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x-neg, y-pos sin&csc=pos

x-pos, y-pos all positive x-pos, y-neg cos &sec=pos

x-neg, y-neg tan & cot=pos

sin=(y/x)

csc=(r/y)

cos=(x/r)

sec=(r/x)

tan=(y/x)

cot=(x/y)

complementary: a+b=90 supplementary: a+b=180 sin(a)+sin(b)=2sin((a+b)/2)cos((a-b)/2) sin(a)-sin(b)=2sin((a-b)/2)cos((a+b)/2) cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2) cos(a)-cos(b)=-2sin((a+b)/2)sin((a-b)/2)

sin(a)sin(b)=.5(cos(a-b)-cos(a+b)) cos(a)cos(b)=.5(cos(a-b)+cos(a+b)) sin(a)cos(b)=.5(sin(a+b)+sin(a-b)) cos(a)sin(b)=.5(sin(a+b)-sin(a-b))

A(t)=(Ao)e^(kt)

f(x)=a((x-h)^2)+k

(Ao)=original amount

a=strech or shirnk, a>0 -->up, a<0 -->down

t=number of years

k=shift h units horizontally

k=rate of change

k=shift k units vertically

y=(a)sin((b)x-(c)pi) a=amp

phase shif=c/b-->-right, +left

period=2pi/b-->sin,cos,sec,csc | pi/b-->tan,cot

cos(-x)=cos(x) & sec(-x)=sec(x)

asymptotes: ver:when denominator=0

sin(-x)=-sin(x) & csc(-x)=-csc(x)

hor:bot>top-->y=0, #s->y=top/bot, top>bot-->none

tan(-x)=-tan(x) & cot(-x)=-cot(x)

slant:expnts top+1=bot-->divide, top+1=bot-->none

|x+n|-y<x+ny-->x+n>y & x+n<-y

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when: z=a+bi |z|=sqrt((a^2)+(b^2))