Math 380
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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