Trigonometry Identities Flashcards

1
Q

1/sin θ

A

csc θ

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2
Q

1/cos θ

A

sec θ

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3
Q

1/tan θ

A

cot θ

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4
Q

1/csc θ

A

sin θ

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5
Q

1/sec θ

A

cos θ

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6
Q

1/cot θ

A

tan θ

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7
Q

sin θ/cos θ

A

tan θ

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8
Q

tan θ cos θ

A

sin θ

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9
Q

sin θ/tan θ

A

cos θ

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10
Q

cos θ/sin θ

A

cot θ

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11
Q

cot θ sin θ

A

cos θ

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12
Q

cos θ/cot θ

A

sin θ

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13
Q

sin² θ + cos² θ

A

1

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14
Q

sin² θ

A

1 - cos² θ

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15
Q

cos² θ

A

1 - sin² θ

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16
Q

1 + tan² θ

A

sec² θ

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17
Q

sec² θ - tan² θ

A

1

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18
Q

tan² θ

A

sec² θ - 1

19
Q

1 + cot² θ

A

csc² θ

20
Q

cot² θ

A

csc² θ - 1

21
Q

csc² θ - cot² θ

A

1

22
Q

sin(-θ)

A

-sin θ

23
Q

csc(-θ)

A

-csc θ

24
Q

cos(-θ)

A

cos θ

25
Q

sec(-θ)

A

sec θ

26
Q

tan(-θ)

A

-tan θ

27
Q

cot(-θ)

A

-cot θ

28
Q

sin 2θ

A

2sin θ cos θ

29
Q

cos 2θ (1/3)

A

cos² θ - sin² θ

30
Q

cos 2θ (2/3)

A

2cos² θ - 1

31
Q

cos 2θ (3/3)

A

1 - 2sin² θ

32
Q

tan 2θ

A

2tan θ/1 - tan² θ

33
Q

sin (ɑ + β)

A

sin ɑ cos β + cos ɑ sin β

34
Q

sin (ɑ - β)

A

sin ɑ cos β - cos ɑ sin β

35
Q

cos (ɑ + β)

A

cos ɑ cos β - sin ɑ sin β

36
Q

cos (ɑ - β)

A

cos ɑ cos β + sin ɑ sin β

37
Q

tan (ɑ + β)

A

tan ɑ + tan β/1 - tan ɑ tan β

38
Q

tan (ɑ - β)

A

tan ɑ - tan β/1 + tan ɑ tan β

39
Q

sin 3θ (1/2)

A

-sin³ θ + 3cos² θ sin θ

40
Q

sin 3θ (2/2)

A

-4sin³ θ + 3sin θ

41
Q

cos 3θ (1/2)

A

cos³ θ - 3sin² θ cos θ

42
Q

cos 3θ (2/2)

A

4cos³ θ - 3cos θ

43
Q

tan 3θ (1/2)

A

3tan θ - tan³ θ/1 - 3tan² θ