# Trig equations

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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))
 Author: tenorsextets ID: 45322 Card Set: Trig equations Updated: 2010-11-15 16:44:18 Tags: Trig trigonometry equations formulas Folders: Description: look at title Show Answers: