Trigonometric Identities Flashcards
1
Q
sinθ (Reciprocal)
A
1/cscθ
2
Q
cosθ (Reciprocal)
A
1/secθ
3
Q
tanθ (Reciprocal)
A
1/cotθ
4
Q
cscθ (Reciprocal)
A
1/sinθ
5
Q
cotθ (Reciprocal)
A
1/tanθ
6
Q
tanθ (Quotient)
A
sinθ/cosθ
7
Q
cotθ (Quotient)
A
cosθ/sinθ
8
Q
sin^2θ + cos^2θ (Pythagorean)
A
1
9
Q
tan^2θ + 1 (Pythagorean)
A
sec^2θ
10
Q
cot^2θ + 1 (Pythagorean)
A
csc^2θ
11
Q
sinθ (Cofunction)
A
cos(π/2-θ)
12
Q
cscθ (Cofunction)
A
sec(π/2-θ)
13
Q
tanθ (Cofunction)
A
cot(π/2-θ)
14
Q
cosθ (Cofunction)
A
sin(π/2-θ)
15
Q
secθ (Cofunction)
A
csc(π/2-θ)
16
Q
cotθ (Cofunction)
A
tan(π/2-θ)
17
Q
sin(-θ) (Even-Odd)
A
-sinθ
18
Q
cos(-θ) (Even-Odd)
A
cosθ
19
Q
tan(-θ) (Even-Odd)
A
-tanθ
20
Q
csc(-θ) (Even-Odd)
A
-cscθ
21
Q
sec(-θ) (Even-Odd)
A
secθ
22
Q
cot(-θ) (Even-Odd)
A
-cotθ
23
Q
sin(A+B) (Sum of Angles)
A
sinA * cosB + cosA * sinB
24
Q
cos(A+B) (Sum of Angles)
A
cosA * cosB - sinA * sinB
25
tan(A+B) (Sum of Angles)
(tanA + tanB)/(1 - tanA*tanB)
26
sin(A-B) (Difference of Angles)
sinA * cosB - cosA * sinB
27
cos(A-B) (Difference of Angles)
cosA * cosB + sinA * sinB
28
tan(A-B) (Difference of Angles)
(tanA - tanB)/(1 + tanA*tanB)
29
sin2θ (Double-Angle)
2sinθ * cosθ
30
cos2θ (Double-Angle)
cos^2θ - sin^2θ
1 - 2sin^2θ
2cos^θ -1
31
tan2θ (Double-Angle)
(2tanθ)/(1-tan^2θ)
32
sin(θ/2) (Half-Angle)
+/- sqrt((1-cosθ)/2)
33
cos(θ/2) (Half-Angle)
+/- sqrt((1+cosθ)/2)
34
tan(θ/2) (Half-Angle)
+/- sqrt((1-cosθ)/(1+cosθ))
(1-cosθ)/(sinθ)
(sinθ)/(1+cosθ)
35
sin^2θ (Power-Reducing)
(1-cos2θ)/2
36
cos^2θ (Power-Reducing)
(1+cos2θ)/2
37
tan^2θ (Power-Reducing)
(1-cos2θ)/(1+cos2θ)
38
sinA * sinB (Product-to-Sum)
1/2[cos(A-B) - cos(A+B)]
39
cosA * cosB (Product-to-Sum)
1/2[cos(A-B) + cos(A+B)]
40
sinA * cosB (Product-to-Sum)
1/2[sin(A-B) + sin(A-B)]
41
cosA * sinB (Product-to-Sum)
1/2[sin(A+B) - sin(A-B)]
42
sinA + sinB (Sum-to-Product)
2 * sin(A+B/2) * cos(A-B/2)
43
cosA + cosB (Sum-to-Product)
2 * cos(A+B/2) * cos(A-B/2)
44
sinA - sinB (Sum-to-Product)
2 * cos(A+B/2) * sin(A-B/2)
45
cosA - cosB (Sum-to-Product)
-2 * sin(A+B/2) * sin(A-B/2)
46
secθ (Reciprocal)
1/cosθ
