| sin(theta) = a / c
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csc(theta) = 1 / sin(theta) = c / a
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cos(theta) = b / c
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sec(theta) = 1 / cos(theta) = c / b
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tan(theta) = sin(theta) / cos(theta) = a / b
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cot(theta) = 1/ tan(theta) = b / a
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sin(-x) = -sin(x)
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csc(-x) = csc(x)
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cos(-x) = cos(x)
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sec(-x) = sec(x)
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tan(-x) = -tan(x)
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cot(-x) = -cot(x)
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sin^2(x) + cos^2(x) = 1
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tan^2(x) + 1 = sec^2(x)
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cot^2(x) + 1 = csc^2(x)
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sin(x y) = sin x cos ycos x sin y
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cos(xy) = cos x cos y sin x sin y
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tan(xy) = (tan xtan y) / (1 tan x tan y)
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sin(2x) = 2 sin x cos x
cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x)
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tan(2x) = 2 tan(x) / (1 - tan^2(x))
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sin^2(x) = 1/2 - 1/2 cos(2x)
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cos^2(x) = 1/2 + 1/2 cos(2x)
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sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )
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cos x - cos y = -2 sin( (x - y)/2 ) sin( (x + y)/2 )
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Trig Table Of Common Angles
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| Angle |
0 |
30 |
45 |
60 |
90 |
| sin^2(a) |
0/4 |
1/4 |
2/4 |
3/4 |
4/4 |
| cos^2(a) |
4/4 |
3/4 |
2/4 |
1/4 |
0/4 |
| tan^2(a) |
0/4 |
1/3 |
2/2 |
3/1 |
4/0 |
Sides a,b,c - Angles A,B,C
a Opposite A, b Opposite B, c Opposite C
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| Law Of Sines
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| a/sin(A) = b/sin(B) = c/sin(C)
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| Law Of Cosines |
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c^2 = a^2 + b^2 - 2ab cos(C)
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b^2 = a^2 + c^2 - 2ac cos(B)
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a^2 = b^2 + c^2 - 2bc cos(A)
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Law Of Tangents
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(a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2]
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