Trigonometric Functions

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39 Terms

1
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If A + B = 180°

sin A = sin B, cos A + cos B = 0, tan A + tan B = 0

2
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If A + B = 90°

sin A = cos B, cos A = sin B

3
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sin(A + B)

sin A cos B + cos A sin B

4
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sin(A - B)

sin A cos B - cos A sin B

5
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cos(A + B)

cos A cos B - sin A sin B

6
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cos(A - B)

cos A cos B + sin A sin B

7
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tan(A + B)

(tan A + tan B) / (1 - tan A tan B)

8
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tan(A - B)

(tan A - tan B) / (1 + tan A tan B)

9
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cot(A + B)

(cot A cot B - 1) / (cot B + cot A)

10
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cot(A - B)

(cot A cot B + 1) / (cot B - cot A)

11
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sin² A - sin² B

sin(A + B) sin(A - B)

12
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cos² A - cos² B

cos(A + B) cos(A - B)

13
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sin 2θ

2 sin θ cos θ = (2 tan θ) / (1 + tan² θ)

14
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cos 2θ

2 cos² θ - 1 = 1 - 2 sin² θ = (1 - tan² θ) / (1 + tan² θ)

15
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tan 2θ

(2 tan θ) / (1 - tan² θ)

16
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sin 3θ

3 sin θ - 4 sin³ θ

17
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cos 3θ

4 cos³ θ - 3 cos θ

18
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tan 3θ

(3 tan θ - tan³ θ) / (1 - 3 tan² θ)

19
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sin(A + B) + sin(A - B)

2 sin A cos B

20
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sin(A + B) - sin(A - B)

2 cos A sin B

21
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cos(A + B) + cos(A - B)

2 cos A cos B

22
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cos(A + B) - cos(A - B)

-2 sin A sin B

23
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sin A + sin B

2 sin((A + B)/2) cos((A - B)/2)

24
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sin A - sin B

2 cos((A + B)/2) sin((A - B)/2)

25
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cos A + cos B

2 cos((A + B)/2) cos((A - B)/2)

26
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cos A - cos B

-2 sin((A + B)/2) sin((A - B)/2)

27
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cos² θ

(1 + cos 2θ) / 2

28
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sin² θ

(1 - cos 2θ) / 2

29
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tan² θ

(1 - cos 2θ) / (1 + cos 2θ)

30
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(cosθ + sinθ)²

1 + sin 2θ

31
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(cosθ - sinθ)²

1 - sin 2θ

32
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tan(π/4 + θ)

(1 + tan θ) / (1 - tan θ)

33
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tan(π/4 - θ)

(1 - tan θ) / (1 + tan θ)

34
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sin(A + B) sin(A - B)

sin² A - sin² B

35
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cos(A + B) cos(A - B)

cos² A - sin² B

36
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tan(A + B + C)

(tan A + tan B + tan C - tan A tan B tan C) / (1 - tan A tan B - tan B tan C - tan C tan A)

37
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sinθ sin(60° - θ) sin(60° + θ)

(1/4) sin 3θ°

38
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cosθ cos(60° - θ) cos(60° + θ)

(1/4) cos 3θ°

39
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tanθ tan(60° - θ) tan(60° + θ)

tan 3θ°