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cos(a+b)
cos(a)cos(b)  sin(a)sin(b)

cos(ab)
cos(a)cos(b) + sin(a)sin(b)

sin(a+b)
sin(a)cos(b) + cos(a)sin(b)

sin(ab)
sin(a)cos(b)  cos(a)sin(b)

tan(ab)
tan(a)tan(b) / 1+tan(a)tan(b)

tan(a+b)
tan(a)+tan(b) / 1tan(a)tan(b)

sin2(a)
 2sin(a)cos(a)
 2cos(a)sin(a)

cos2(a)
 •cos^2(a)  sin^2(a)
 •1  2sin^2(a)
 •2cos^2(a)  1

tan2(a)
2tan(a) / 1  tan^2(a)



tan(a/2)
 sin(a)/1+cos(a)
 1cos(a)/sin(a)
 ±√[(1cos(a)/1+cos(a)]

Law of Sines
sin(A)/a = sin(B)/b = sin(C)/c

Law of Cosines
a^2 = b^2 + c^2  2(a)(b)cos(A)

Heron's Fomula (find the area of a triangle given 3 sides)
 √[s(sa)(sb)(sc)]
 s= 1/2(a+b+c)

What is the magnitude of a vector?
 The length of the line that is made.
 V= <4,2>= 4i + 2j

Magnitude of a vector
V= √[a^2 + b^2] < Pythagorean theorem

With imaginary numbers, the x and y axis become the _____ and ______ axis, respectively.
Imaginary and Real

When adding two vectors the result r is
the line that can be drawn between the endpoints of each vector.

Dot Product of two vectors
v • w= ac + bd

Angle between two vectors
cosθ= (u•v)÷(mag. u)(mag. v)

Unit Vector=
magnitude of 1

Formula to find unit vector
u= <vector> / mag. v

imaginary number i=
√[1]


trig form of complex number equation z=x + yi
z= r(cosθ)+r(sinθ)= r(cosθ+sinθ)

For complex numbers:
sinθ=
cosθ=
tanθ=
 y/r ; y=r(sinθ)
 x/r ; x=r(cosθ)
 y/x

How do you find r for a complex number equation?
 Magnitude of z:
 z= √[x^2 + y^2]

How is the argument (angle) measured?
ALWAYS fromt the positive xaxis.

To multiply complex number equations:
multiply the modulus (r) and add the argument (the angles on the cosine and sine in the parenthesis).

To divide complex number equations:
divide the modulus (r) and subtract the argument (the angles on the cosine and sine in the parenthesis).

Demovire's theorem (multiplying a complex number equation by itself)
z^n= r^n(cos(nθ) + i sin(nθ))

