Trig equations

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tenorsextets
ID:
45322
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Trig equations
Updated:
2010-11-15 11:44:18
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Trig trigonometry equations formulas
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  1. cos(a+b)
    cos(a)cos(b) - sin(a)sin(b)
  2. cos(a-b)
    cos(a)cos(b) + sin(a)sin(b)
  3. sin(a+b)
    sin(a)cos(b) + cos(a)sin(b)
  4. sin(a-b)
    sin(a)cos(b) - cos(a)sin(b)
  5. tan(a-b)
    tan(a)-tan(b) / 1+tan(a)tan(b)
  6. tan(a+b)
    tan(a)+tan(b) / 1-tan(a)tan(b)
  7. sin2(a)
    • 2sin(a)cos(a)
    • 2cos(a)sin(a)
  8. cos2(a)
    • •cos^2(a) - sin^2(a)
    • •1 - 2sin^2(a)
    • •2cos^2(a) - 1
  9. tan2(a)
    2tan(a) / 1 - tan^2(a)
  10. sin(a/2)
    √[1-cos(a)] / 2
  11. cos(a/2)
    √[1+cos(a)] / 2
  12. tan(a/2)
    • sin(a)/1+cos(a)
    • 1-cos(a)/sin(a)
    • ±√[(1-cos(a)/1+cos(a)]
  13. Law of Sines
    sin(A)/a = sin(B)/b = sin(C)/c
  14. Law of Cosines
    a^2 = b^2 + c^2 - 2(a)(b)cos(A)
  15. Heron's Fomula (find the area of a triangle given 3 sides)
    • √[s(s-a)(s-b)(s-c)]
    • s= 1/2(a+b+c)
  16. What is the magnitude of a vector?
    • The length of the line that is made.
    • V= <4,2>= 4i + 2j
  17. Magnitude of a vector
    |V|= √[a^2 + b^2] <--- Pythagorean theorem
  18. With imaginary numbers, the x and y axis become the _____ and ______ axis, respectively.
    Imaginary and Real
  19. When adding two vectors the result r is
    the line that can be drawn between the endpoints of each vector.
  20. Dot Product of two vectors
    v • w= ac + bd
  21. Angle between two vectors
    cosθ= (u•v)÷(|mag. u|)(|mag. v|)
  22. Unit Vector=
    magnitude of 1
  23. Formula to find unit vector
    u= <vector> / |mag. v|
  24. imaginary number i=
    √[-1]
  25. i^2=
    i^4=
    • -1
    • 1
  26. trig form of complex number equation z=x + yi
    z= r(cosθ)+r(sinθ)= r(cosθ+sinθ)
  27. For complex numbers:
    sinθ=
    cosθ=
    tanθ=
    • y/r ; y=r(sinθ)
    • x/r ; x=r(cosθ)
    • y/x
  28. How do you find r for a complex number equation?
    • Magnitude of z:
    • |z|= √[x^2 + y^2]
  29. How is the argument (angle) measured?
    ALWAYS fromt the positive x-axis.
  30. To multiply complex number equations:
    multiply the modulus (r) and add the argument (the angles on the cosine and sine in the parenthesis).
  31. To divide complex number equations:
    divide the modulus (r) and subtract the argument (the angles on the cosine and sine in the parenthesis).
  32. Demovire's theorem (multiplying a complex number equation by itself)
    z^n= r^n(cos(nθ) + i sin(nθ))

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