Trignometry
Curves   Imaginary math   Math   Calculus   Area & Volume

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
sum of sine and cos
Acosωt + Bsinωt = (√(A²+B²))cos(ωt–arctan(B/A))

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