Trigonometry Flashcards
(38 cards)
1
Q
sin^2θ + cos^2θ
A
1
2
Q
1 + tan^2θ
A
sec^2θ
3
Q
1+cot^2θ
A
cosec^2θ
4
Q
sin^4θ + cos^4θ
A
1-2sin^2θcos^2θ
5
Q
sin^6θ + cos^6θ
A
1-3sin^2θcos^2θ
6
Q
sin(A+B)
A
sinAcosB+cosAsinB
7
Q
sin(A-B)
A
sinAcosB-cosAsinB
8
Q
cos(A+B)
A
cosAcosB-sinAsinB
9
Q
cos(A-B)
A
cosAcosB+sinAsinB
10
Q
tan(A+B)
A
(tanA+tanB)/1-tanAtanB
11
Q
tan(A-B)
A
(tanA-tanB)/1+tanAtanB
12
Q
cot(A+B)
A
cotAcotB-1/cotA+cotB
13
Q
cot(A-B)
A
cotAcotB+1/cotA-cotB
14
Q
2sinAcosB
A
sin(A+B) + sin(A-B)
15
Q
2cosAsinB
A
sin(A+B)-sin(A-B)
16
Q
2cosAcosB
A
cos(A+B)+cos(A-B)
17
Q
2sinAsinB
A
cos(A-B)-cos(A+B)
18
Q
sin2θ
A
2sinθcosθ
19
Q
cos2θ
A
2cos^2θ-1
or
1-2sin^2θ
20
Q
tan2θ
A
2tanθ/1-tan^2θ
21
Q
sin3θ
A
3sinθ-4sin^3θ
22
Q
cos3θ
A
4cos^3θ-3cosθ
23
Q
tan3θ
A
3tanθ-tan^3θ/1 - 3tan^2θ
24
Q
sinθsin(60-θ)sin(60+θ)
A
sin3θ/4
25
cosθcos(60-θ)cos(60+θ)
cos3θ/4
26
tanθtan(60-θ)tan(60+θ)
tan3θ
27
cotθcot(60-θ)cot(60+θ)
cot3θ
28
tanθ+tan(60+θ)+tan(60-θ)
3tan3θ
29
Range of sin and cos function
[-1,1]
30
Range of cot and tan function
(-∞, ∞)
31
Range of sec and cosec function
(-∞, -1]∪[1, ∞)
32
General Form of Angle of any sin function
x = nπ + (-1)^nα, where n belongs to integer
33
General Form of Angle of any cos function
x = 2nπ±α, where n belongs to integer
34
General Form of Angle of any tan function
x = nπ+α, where n belongs to integer
35
General Form of Angle of any sin^2, cos^2 and tan^2 function
x = nπ±α, where n belongs to integer
36
Principal Solution
Solution of trigonometric equation lying in the interval [0, 2π)
37
General Solution
Solutions represented using a general formula
38
Particular Solution
Solutions of trigonometric equations lying in the particular interval
