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Math 380

Terms

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Length of a circular arc
s=r((theta))
Area of a Circular Sector
A=(1/2)r^2((theta))
Angular Speed
w=((theta))/t
Linear Speed
v=s/t
Relationship between lin. and ang. speed
linear speed=r(angular speed)
pythagorean identity
sin^2(x)+cos^2(x)=1
Area of a triangle (trig)
A=1/2 ab sin ((theta))
Law of Sines
SinA/a = SinB/b = SinC/c
Law of Cosines
a^2=b^2 + c^2 - 2bc cosA
Cofunction Identities
sin(pi/2 - u)=cosu
even odd
sin(-x)=-sinx cos(-x)= cosx tan(-x)= -tanx
addition subtraction
sin(s+t)= sinscost + coss sint cos(s+t)= cosscost - sinssint tan(s+t)=( tans+tant)/1-tanstant
double angle
sin2x= 2sinxcosx cos2x= cos^2x-sin^2x =2cos^2x -1 =1-2sin^2x tan2x= (2tanx)/(1-tan^2x)
lowering power
sin^2x=(1-cos2x)/2 cos^2x=(1+cos2x)/2 tan^2x= (1-cos2x)/(1+cos2x)
half angle
sin(u/2)= (+/-)√((1-cosu)/2) cos(u/2)= same except plus plus or minus based on quadrent of u/2
Polar to rect
x=rcos((theta)) y=rsin((theta))
rect to polar
r^2=x^2+y^2 tan((theta))=y/x
modulus of a complex #
|z|= √a^2+b^2
polar form of complex #
z=a+bi z=rcis((theta))
Mult. and Div. of complex numbers
z1=r1cis((theta1)) z2=r2cis((theta2)) z1z2=r1r2(cis(((theta1))+((theta2))) div: signs switched
demoivres theorem
z^n=r^ncisn((theta))
horz. and vert. components of a vector
v=|v|cos((theta))i + |v|sin((theta))j
angle between two vectors
cos((theta))= (U * V)/|U||V|
orthogonal vectors
u * v = 0
component of u along v
(u * v)/|v|
projection of u along v
((u * v)/|v|^2)v

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caminator71

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