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Level 531

Trigonometric Triangles & Polar Coordinates


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cosθ
Adj/Hyp
sinθ
Opp/Hyp
tanθ
Opp/Adj
secθ
1/cosθ
cscθ
1/sinθ
cotθ
tan(π/2 - θ)
A+B=90
Complementary Theorem
SAA or ASA
One side and two angles. Use law of Sines.
SSA
Side-Side-Angle
SAS
b²=a²+c²-2acCosB
SSS
Side-Side-Side
Law of Sines
Sin A/a=Sin B/b=Sin C/c
C^2=a^2+b^2-2abcosC
Law of cosine 3
d
2rsin(θ/2)
A=(1/2)bh
Area of a triangle
Area=(1/2)absinC
Trig Area of a Triangle
A=√s(s-a)(s-b)(s-c)
Area of a Triangle (use the side lengths)
(a+b+c)/2
S (semi-perimeter)
d(t)=acos(Ѡt)
Harmonic Motion Distance
d=ae^(-bt/2m)cos(√Ѡ^2-(b^2/4m^2)t)
Damped Oscillatory Motion
Polar Coordinate Point
(r,θ+2πk), or (-r,θ+π+2πk)
|z|=√x^2+y^2
Magnitude Modulus
z=x+yi
Cartesian Form
(rcosθ)+(rsinθ)i
Polar Form
z^n=r^nCiS(nθ)
DeMoivre's Theorem