Trigonometry Identities & Formulas

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Pre-Calculus

9th

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49 Terms

1

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<p>sinθ / cosθ</p>

sinθ / cosθ

tanθ

<p>tanθ</p>

2

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<p>cosθ / sinθ</p>

cosθ / sinθ

cotθ

<p>cotθ</p>

3

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<p>1 / cscθ</p>

1 / cscθ

sinθ

<p>sinθ</p>

4

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<p>1 / sinθ</p>

1 / sinθ

cscθ

<p>cscθ</p>

5

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<p>1 / secθ</p>

1 / secθ

cosθ

<p>cosθ</p>

6

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<p>1 / cosθ</p>

1 / cosθ

secθ

<p>secθ</p>

7

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<p>1 / cotθ</p>

1 / cotθ

tanθ

<p>tanθ</p>

8

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<p>1 / tanθ</p>

1 / tanθ

cotθ

<p>cotθ</p>

9

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<p>sin<sup>2</sup>θ + cos<sup>2</sup>θ</p>

sin²θ + cos²θ

1

<p>1</p>

10

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<p>tan<sup>2</sup>θ + 1</p>

tan²θ + 1

sec²θ

<p>sec<sup>2</sup>θ</p>

11

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<p>1 + cot<sup>2</sup>θ</p>

1 + cot²θ

csc²θ

<p>csc<sup>2</sup>θ</p>

12

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<p>sin(-θ)</p>

sin(-θ)

-sinθ

<p>-sinθ</p>

13

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<p>csc(-θ)</p>

csc(-θ)

-cscθ

<p>-cscθ</p>

14

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<p>cos(-θ)</p>

cos(-θ)

cosθ

<p>cosθ</p>

15

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<p>sec(-θ)</p>

sec(-θ)

secθ

<p>secθ</p>

16

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<p>tan(-θ)</p>

tan(-θ)

-tanθ

<p>-tanθ</p>

17

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<p>cot(-θ)</p>

cot(-θ)

-cotθ

<p>-cotθ</p>

18

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<p>sin(θ + 2πn)</p>

sin(θ + 2πn)

sinθ

<p>sinθ</p>

19

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<p>csc(θ + 2πn)</p>

csc(θ + 2πn)

cscθ

<p>cscθ</p>

20

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<p>cos(θ + 2πn)</p>

cos(θ + 2πn)

cosθ

<p>cosθ</p>

21

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<p>sec(θ + 2πn)</p>

sec(θ + 2πn)

secθ

<p>secθ</p>

22

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<p>tan(θ + πn)</p>

tan(θ + πn)

tanθ

<p>tanθ</p>

23

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<p>cot(θ + πn)</p>

cot(θ + πn)

cotθ

<p>cotθ</p>

24

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<p>2sinθcosθ</p>

2sinθcosθ

sin(2θ)

<p>sin(2θ)</p>

25

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<p>= cos<sup>2</sup>θ - sin<sup>2</sup>θ</p><p>= 2cos<sup>2</sup>θ - 1</p><p>= 1 - 2sin<sup>2</sup>θ</p>

= cos²θ - sin²θ

= 2cos²θ - 1

= 1 - 2sin²θ

cos(2θ)

<p>cos(2θ)</p>

26

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<p>2tanθ / 1 - tan<sup>2</sup>θ</p>

2tanθ / 1 - tan²θ

tan(2θ)

<p>tan(2θ)</p>

27

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<p>± √(1-cos(2θ))/2</p>

± √(1-cos(2θ))/2

sinθ

<p>sinθ</p>

28

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<p>± √(1-cosθ)/2</p>

± √(1-cosθ)/2

sinθ/2

<p>sinθ/2</p>

29

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<p>± √(1+cos(2θ))/2</p>

± √(1+cos(2θ))/2

cosθ

<p>cosθ</p>

30

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<p>± √(1+cosθ)/2</p>

± √(1+cosθ)/2

cosθ/2

<p>cosθ/2</p>

31

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<p>± √(1-cos2θ)/(1+cos2θ)</p>

± √(1-cos2θ)/(1+cos2θ)

tanθ

<p>tanθ</p>

32

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<p>= ± √(1-cosθ)/(1+cosθ)</p><p>= sinθ / 1+cosθ</p><p>= 1-cosθ / sinθ</p>

= ± √(1-cosθ)/(1+cosθ)

= sinθ / 1+cosθ

= 1-cosθ / sinθ

tanθ/2

<p>tanθ/2</p>

33

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<p>sin<span><span>αcos</span></span>β <span><span>± cos</span></span><span>αsin</span>β</p>

sinαcosβ ± cosαsinβ

sin(α ± β)

<p>sin(<span>α ± </span>β)</p>

34

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<p>cos<span>αcos</span>β <span><span>∓</span></span><span> sinαsin</span>β</p>

cosαcosβ ∓ sinαsinβ

cos(α ± β)

<p>cos(<span>α ± </span>β)</p>

35

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<p>tan<span>αtan</span>β <span>± tanαtan</span>β / 1 <span>∓ tanαtan</span>β</p>

tanαtanβ ± tanαtanβ / 1 ∓ tanαtanβ

tan(α ± β)

<p>tan(<span>α ± </span>β)</p>

36

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<p>1/2[cos(<span>α-</span>β) - cos(<span>α+</span>β)]</p>

1/2[cos(α-β) - cos(α+β)]

sinαsinβ

<p><span>sinαsin</span>β</p>

37

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<p>1/2[cos(<span>α-</span>β) + cos(<span>α+</span>β)]</p>

1/2[cos(α-β) + cos(α+β)]

cosαcosβ

<p><span>cosαcos</span>β</p>

38

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<p>1/2[sin(<span>α+</span>β) + sin(<span>α-</span>β)]</p>

1/2[sin(α+β) + sin(α-β)]

sinαcosβ

<p><span>sinαcos</span>β</p>

39

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<p>1/2[sin(<span>α+</span>β) - sin(<span>α-</span>β)]</p>

1/2[sin(α+β) - sin(α-β)]

cosαsinβ

<p><span>cosαsin</span>β</p>

40

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<p>2sin((<span>α+</span>β)/2)cos((<span>α-</span>β)/2)</p>

2sin((α+β)/2)cos((α-β)/2)

sinα + sinβ

<p><span>sinα + sin</span>β</p>

41

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<p>2cos((<span>α+</span>β)/2)sin((<span>α-</span>β)/2)</p>

2cos((α+β)/2)sin((α-β)/2)

sinα - sinβ

<p><span>sinα - sin</span>β</p>

42

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<p>2cos((<span>α+</span>β)/2)cos((<span>α-</span>β)/2)</p>

2cos((α+β)/2)cos((α-β)/2)

cosα + cosβ

<p><span>cosα + cos</span>β</p>

43

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<p>-2sin((<span>α+</span>β)/2)sin((<span>α-</span>β)/2)</p>

-2sin((α+β)/2)sin((α-β)/2)

cosα - cosβ

<p><span>cosα - cos</span>β</p>

44

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<p>sin(π/2 - θ)</p>

sin(π/2 - θ)

cosθ

<p>cosθ</p>

45

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<p>cos(π/2 - θ)</p>

cos(π/2 - θ)

sinθ

<p>sinθ</p>

46

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<p>csc(π/2 - θ)</p>

csc(π/2 - θ)

secθ

<p>secθ</p>

47

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<p>sec(π/2 - θ)</p>

sec(π/2 - θ)

cscθ

<p>cscθ</p>

48

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<p>tan(π/2 - θ)</p>

tan(π/2 - θ)

cotθ

<p>cotθ</p>

49

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<p>cot(π/2 - θ)</p>

cot(π/2 - θ)

tanθ

<p>tanθ</p>