Trig Identities Flashcards
1
Q
sin(A+B)
A
sin(A)cos(B) + cos(A)sin(B)
2
Q
sin(A-B)
A
sin(A)cos(B) - cos(A)sin(B)
2
Q
cos(A+B)
A
cos(A)cos(B) - sin(A)sin(B)
3
Q
cos(A-B)
A
cos(A)cos(B) + sin(A)sin(B)
4
Q
tan(A+B)
A
[tan(A) + tan(B)]/[1 - tan(A)tan(B)]
5
Q
tan(A-B)
A
[tan(A) - tan(B)]/[1 + tan(A)tan(B)]
6
Q
tan(θ)
A
sin(θ)/cos(θ)
7
Q
cot(θ)
A
cos(θ)/sin(θ)
8
Q
sin²θ + cos²θ
A
1
9
Q
sec²θ - tan²θ
A
1
10
Q
csc²θ - cot²θ
A
1
11
Q
sin(-θ)
A
-sin(θ)
12
Q
tan(-θ)
A
-tan(θ)
13
Q
csc(-θ)
A
-csc(θ)
14
Q
cos(-θ)
A
cos(θ)
15
Q
cot(-θ)
A
-cot(θ)
16
Q
sec(-θ)
A
sec(θ)
17
Q
sin(π/2 - θ)
A
cos(θ) (and vice versa)
18
Q
tan(π/2 - θ)
A
cot(θ) (and vice versa)
19
Q
csc(π/2 - θ)
A
sec(θ) (and vice versa)
20
Q
sin(2θ)
A
2sin(θ)cos(θ)
21
Q
cos(2θ)
A
cos²θ - sin²θ or 2cos²θ -1 or 1 - 2sin²θ
22
Q
tan(2θ)
A
(2tanθ)/(1 - tan²θ)
23
Q
sin²θ
A
[1 - cos(2θ)]/2
24
cos²θ
[1 + cos(2θ)]/2
25
tan²θ
[1 - cos(2θ)]/[1 + cos(2θ)]
26
sinA + sinB
2sin[(A+B)/2]cos[(A-B)/2]
27
sinA - sinB
2cos[(A+B)/2]sin[(A-B)/2]
28
cosA + cosB
2cos[(A+B)/2]cos[(A-B)/2]
29
cosA - cosB
-2sin[(A+B)/2]sin[(A-B)/2]
30
sin(A)sin(B)
[cos(A-B) - cos(A+B)]/2
31
cos(A)cos(B)
[cos(A-B) + cos(A+B)]/2
32
sin(A)cos(B)
[sin(A+B) + sin(A-B)]/2
33
cos(A)sin(B)
[sin(A+B) - sin(A-B)]/2
