Trig identities Flashcards
1
Q
tan (x) =
A
sin(x) / cos(x)
2
Q
cot(x)=
A
cos(x) / sin(x)
or
1/tan(x)
3
Q
sec(x)=
A
1/cos(x)
4
Q
csc(x)=
A
1/sin(x)
5
Q
What is the Pythagorean identity?
A
sin^2(x) + cos^2(x)= 1
6
Q
cos^2(x)=
A
1-sin^2(x)
7
Q
sin^2(x)=
A
1-cos^2(x)
8
Q
csc^2(x)=
A
1+cot^2(x)
9
Q
sec^2(x)=
A
1+tan^2(x)
10
Q
sin(2x)
A
2sin(x)cos(x)
11
Q
cos(2x)
A
cos^2(x) - sin^2(x)
or
2cos^2(x)-1
or
1-2sin^2(x)
12
Q
tan(2x)=
A
2tan(x) / (1-tan^2(x))
13
Q
sin (x/2)=
A
√(1-cos(x)) / 2
14
Q
cos (x/2) =
A
√(1+cos(x)) / 2
15
Q
tan (x/2) =
A
(1-cos(x)) / sin(x)
sin(x) / (1+cos(x))
√(1-cos(x) / 1+ cos(x)
16
Q
cos (A + B)
A
cos(A)cos(B)-sin(A)sin(B)
17
Q
sin (A+B)
A
sin (A)cos(B) - cos(A)sin(B)
18
Q
sin^2(x) (double angle)
A
1/2 (1-cos(2A))
19
Q
cos^2(A) (half angle) =
A
1/2 (1+cos(2A)
20
Q
Sin(A)sin(B) =
A
1/2 (cos(A-B) - cos(A+B))
21
Q
cos(A)cos(B)=
A
1/2 (cos(A-B)+cos(A+B))
22
Q
sinAcosB
A
1/2 (sin(A-B) + sin (A+B)
23
Q
sin’(x)
A
cos(x)
24
Q
cos’(x)
A
-sin (x)
25
tan' (X)
sec^2(x)
26
sec'(x)
sec(x)tan(x)
27
csc'(x)
-csc(x)cot(x)
28
cot'(x)
-csc^2(x)
29
∫sin(x) dx
-cos(x) + C
30
∫ cos(x)dx
sin (x) +C
31
∫ tan(x) dx=
ln|sec(x)| + C
32
∫csc(x) dx
ln |csc(x) -cot(x)| +C
33
∫sec(x) dx
ln |secx) + tan(x)| +C
34
∫cot(x) dx
-ln |csc(x)| + C
35
what is the range of arc cos, arc cot, arc sec ?
(0,π)
36
what is the rang of arcsin, arctan, arc csc?
(π/2, -π/2)
