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``` 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 Home Area, Volume Atomic Mass Black Body Radiation Boolean Algebra Calculus Capacitor Center of Mass Carnot Cycle Charge Chemistry   Elements   Reactions Circuits Complex numbers Constants Curves, lines deciBell Density Electronics Elements Flow in fluids Fourier's Law Gases Gravitation Greek Alphabet Horizon Distance Interest Magnetics Math   Trig Math, complex Maxwell's Eq's Motion Newton's Laws Octal/Hex Codes Orbital Mechanics Particles Parts, Analog IC   Digital IC   Discrete Pendulum Planets Pressure Prime Numbers Questions Radiation Refraction Relativistic Motion Resistance, Resistivity Rotation Series SI (metric) prefixes Skin Effect Specific Heat Springs Stellar magnitude Thermal Thermal Conductivity Thermal Expansion Thermodynamics Trigonometry Units, Conversions Vectors Volume, Area Water Wave Motion Wire, Cu   Al   metric Young's Modulus