trig identities
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Last updated 1:25 AM on 1/31/23
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27 Terms
1
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sin(−𝜃) \=
− sin 𝜃
2
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cos(−𝜃) \=
cos 𝜃
3
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tan(−𝜃) \=
− tan 𝜃
4
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csc(−𝜃) \=
− csc 𝜃
5
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sec(−𝜃) \=
sec 𝜃
6
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cot(−𝜃) \=
− cot 𝜃
7
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tan 𝜃 \=
sin 𝜃/cos 𝜃
8
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cot 𝜃 \=
cos 𝜃/sin 𝜃
9
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sin^2 𝜃 + cos^2 𝜃 \=
1
10
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tan^2 𝜃 + 1 \=
sec^2 𝜃
11
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cot^2 𝜃 + 1 \=
csc^2 𝜃
12
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sin 2𝜃
\= 2 sin 𝜃cos 𝜃
13
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cos 2𝜃
\= cos^2 𝜃 − sin^2 𝜃
14
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cos 2𝜃
\= 2 cos^2 𝜃 − 1
15
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cos 2𝜃
\= 1 − 2 sin^2 𝜃
16
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tan 2𝜃
\= 2 tan 𝜃/1 − tan2
17
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sin(𝐴± 𝐵) \=
sin 𝐴 cos𝐵 ± cos 𝐴 sin 𝐵
18
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cos(𝐴± 𝐵) \=
cos𝐴 cos 𝐵 ∓ sin 𝐴 sin𝐵
19
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tan(𝐴 ± 𝐵) \=
(tan 𝐴 ± tan𝐵)/(1 ∓ tan𝐴 tanB)
20
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sin 𝐴 sin 𝐵 \=
1/2 [cos(𝐴 − 𝐵) − cos(𝐴 + 𝐵)]
21
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cos 𝐴 cos 𝐵 \=
1/2[cos(𝐴 + 𝐵) + cos(𝐴 − 𝐵)]
22
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sin 𝐴 cos 𝐵 \=
1/2 [sin(𝐴 + 𝐵) + sin(𝐴 − 𝐵)]
23
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cos 𝐴 sin 𝐵 \=
1/2 [sin(𝐴 + 𝐵) − sin(𝐴 − 𝐵)
24
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sin𝐴 + sin𝐵 \=
2 sin[(𝐴+𝐵)/2] cos [(𝐴−𝐵)/2]
25
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sin𝐴 − sin𝐵 \=
2 cos [(𝐴+𝐵)/2]sin[(𝐴−𝐵)/2]
26
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cos𝐴 + cos𝐵 \=
2 cos [(𝐴+𝐵)/2] cos [(𝐴−𝐵)/2]
27
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cos𝐴 − cos𝐵 \=
−2 sin [(𝐴+𝐵)/2]sin[(𝐴− 𝐵)/2]
Note 
Flashcards (20)