Trignometry
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General
Supplementary angles are pairs of angles that add up to 180º
complementary angles are pairs of angles that add up to 90°
cofunctions of complementary angles are equal, eg sin-cos, tan-cot

sinθ = opposite/hypotenuse   cscθ = 1/sinθ = h/o
cosθ = adjacent/hypotenuse   secθ = 1/cosθ = h/a
tanθ = opposite/adjacent     cotθ = 1/tanθ = a/o

tanθ = sinθ / cosθ
cotθ = cosθ / sinθ
cscθ = 1 / sinθ
secθ = 1 / cosθ
cotθ = 1 / tanθ

sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
cot²θ + 1 = csc²θ
sin(–θ) = –sinθ    csc(–θ) = –cscθ
cos(–θ) = cosθ     sec(–θ) = secθ
tan(–θ) = –tanθ    cot(–θ) = –cotθ
sinθ = –cos(θ+π/2)
cosθ = sin(θ+π/2)
sinθ = –sin(θ+π)
cosθ = –cos(θ+π)
sin2θ = 2sinθcosθ
cos2θ = cos²θ – sin²θ = 2cos²θ – 1
tan2θ = 2tanθ / (1 – tan²θ)
cos(θ ± φ) = cosθ cosφ ∓ sinθ sinφ
sin(θ ± φ) = sinθ cosφ ± cosθ sinφ
tan(θ ± φ) = (tanθ ± tanφ) / (1 ∓ tanθ tanφ)
cot(θ ± φ) = (cotθ cotφ ∓ 1) / (cotφ ± cotθ)

Sine wave
v = V sin ωt = V sin 2πft
where t is time in sec
ω is angular frequency
f is frequency in Hz
V is peak voltage
v is instantaneous voltage
T is period of sine wave
ω = 2πf
T = 1/f
RMS voltage = V/√2

Radians and degrees
2π radians = 360º = 1 circle

Function values
    angle      sin    cos    tan    cot
  0º             0      1      0      ∞
 30º    π/6    1/2   √3/2   1/√3     √3
 45º    π/4   1/√2   1/√2      1      1
 60º    π/3   √3/2    1/2     √3   1/√3
 90º    π/2      1      0      ∞      0
120º   2π/3   √3/2   –1/2    –√3  –1/√3
135º   3π/4   1/√2  –1/√2     –1     –1
150º   5π/6    1/2  –√3/2  –1/√3    –√3
180º      π      0     –1      0      ∞
210º   7π/6   –1/2  –√3/2   1/√3     √3
225º   5π/4  –1/√2  –1/√2      1      1
240º   4π/3  –√3/2   –1/2     √3   1/√3
270º   3π/2     –1      0      ∞      0
300º   5π/3  –√3/2    1/2    –√3  –1/√3
315º   7π/4  –1/√2   1/√2     –1     –1
330º  11π/6   –1/2   √3/2  –1/√3    –√3
360º     2π      0      1      0      ∞

     angle      sin    cos    tan    cot
  –0º             0      1      0      ∞
 –30º   –π/6   –1/2   √3/2  –1/√3    –√3
 –45º   –π/4  –1/√2   1/√2     –1     –1
 –60º   –π/3  –√3/2    1/2    –√3  –1/√3
 –90º   –π/2     –1      0      ∞      0
–120º  –2π/3  –√3/2   –1/2     √3   1/√3
–135º  –3π/4  –1/√2  –1/√2      1      1
–150º  –5π/6   –1/2  –√3/2   1/√3     √3
–180º     –π      0     –1      0      ∞
–210º  –7π/6    1/2  –√3/2  –1/√3    –√3
–225º  –5π/4   1/√2  –1/√2     –1     –1
–240º  –4π/3   √3/2   –1/2    –√3  –1/√3
–270º  –3π/2      1      0      ∞      0
–300º  –5π/3   √3/2    1/2     √3   1/√3
–315º  –7π/4   1/√2   1/√2      1      1
–330º –11π/6    1/2   √3/2   1/√3     √3
–360º    –2π      0      1      0      ∞


    angle      sin           cos
 15º   π/12  (√6–√2)/4      (√6+√2)/4
 18º   π/10  (√5–1)/4       (√(10+2√5))/4
 36º   π/5   (√(10–2√5))/4  (√5+1)/4
 54º  3π/10  (√5+1)/4       (√(10–2√5))/4
 72º  2π/5   (√(10+2√5))/4  (√5–1)/4
 75º  5π/12  (√6+√2)/4      (√6–√2)/4

1/√2 = 0.707        √3 = 1.732
√3/2 = 0.877      1/√3 = 0.577

cosine rule
law of cosines relates the lengths of the sides of a plane triangle to the cosine of one of its angles. If a, b, c are the three sides of a triangle, and C is the angle between a and b and opposite side c, then:
c² = a² + b² – 2abcosC
or cos C = (a² + b² – c²) / (2ab)
cos A = (b² + c² – a²) / (2bc)
cos B = (a² + c² – b²) / (2ac)
if the ratio is nagative, that means angle is obtuse, between 90º and 180º

Sine rule
law of sines (also known as the sine formula or sine rule) relates the lengths of the sides of a plane triangle to the sine of its angles.
a,b,c are the lengths of the sides
A,B,C are the opposite angles
a/sinA = b/sinB = c/sinC

note that
a/sinA = b/sinB = c/sinC = 2R
where R is the radius of a circumscised circle
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