Trig Identities Flashcards
1
Q
derivative of sin(x)
A
cos(x)
2
Q
derivative of cos(x)
A
-sin(x)
3
Q
integral of 1/(1+x^2)
A
arctanx
4
Q
derivative of arctanx
A
1/(1+x^2)
5
Q
derivative of tan(x)
A
sec(x)^2
5
Q
integral of sec(x)^2
A
tan(x)
6
Q
derivative of sec(x)
A
sec(x)tan(x)
7
Q
integral of sec(x)tan(x)
A
sec(x)
8
Q
derivative of tan(x)^2
A
2tan(x)sec(x)^2
9
Q
integral of 2tan(x)sec(x)^2
A
tan(x)^2
10
Q
derivative of sin(x)^2
A
2sin(x)cos(x)
11
Q
integral of 2sin(x)cos(x)
A
sin(x)^2
12
Q
derivative of csc(x)^2
A
-2cot(x)csc(x)^2
13
Q
integral of -2cot(x)csc(x)^2
A
csc(x)^2
14
Q
derivative of ln(x)
A
1/x
15
Q
integral of 1/x
A
ln(x)
16
Q
sec(x)^2=?
A
tan^2+1
17
Q
cos(x)^2+sin(x)^2=?
A
1
18
Q
tan(x)^2
A
sec(x)^2-1
19
Q
sin(2x)
A
2sin(x)cos(x)
20
Q
cos(2x)
A
2cos(x)^2-1
21
Q
cos(x)^2
A
1+cos(2x)/2
22
Q
sin(x)^2
A
(1 - cos(2x))/2
23
Q
1 + cot²(x)
A
csc²(x)
24
cot²(x)
csc²(x) - 1
25
∫cos(x)dx
sin(x) + C
26
∫sin(x)dx
-cos(x) + C
27
∫sec²(x)dx
tan(x) + C
28
∫csc²(x)dx
-cot(x) + C
29
∫sec(x)tan(x)dx
sec(x) + C
30
∫csc(x)cot(x)dx
-csc(x) + C
31
∫tan(x)dx
ln|sec(x)| + C
32
∫cot(x)dx
ln|sin(x)| + C
33
∫sec(x)dx
ln|sec(x)-tan(x)| + C
34
∫csc(x)dx
ln|csc(x)-cot(x)| + C
35
√(a²-x²)
asinΘ
36
√(x²+a²)
atanΘ
37
√(x²-a²)
asecΘ
38
odd power of sin/cos
split off sin(x), u = cos(x)
39
even power of sin/cos
split off sin^2(x), use (1-cos2x)/2
40
even power of sec
split off sec^2(x), u = tan(x)
41
odd power of sec/tan
split of tan(x)sec(x), u = sec(x)
42
