Trig Rules Flashcards
1
Q
∫sec(x)tan(x)
A
sec(x) + C
2
Q
∫csc(x) cot(x)
A
-csc(x) +C
3
Q
∫csc²(x)
A
-cot(x) + C
4
Q
∫tan(x)
A
ln| sec(x)| +C
5
Q
∫sec(x)
A
ln |sec(x) + tan(x)| +C
6
Q
∫1/(a² +x²)
A
1/a tan−1(x/a) +C
7
Q
∫ 1/ √(a- x²)
A
sin−1( x/a) +C
8
Q
∫ ln(x)
A
xln(x) -x +C
9
Q
(sec(x))’
A
sec(x)tan(x)
10
Q
(csc(x))’
A
-csc(x) cot(x)
11
Q
(cot(x))’
A
-csc² (x)
12
Q
∫a^x
A
1/ln(a)*a^x
13
Q
(cos-1(x))’
A
-1/√(1-x²)
14
Q
(tan-1(x))’
A
1/(1+x²)
15
Q
lim x–>0 (sin(x)/x)
A
1
16
Q
lim x–>0 (cos(x) -1)/x
A
0
17
Q
lim x–> 0 sin(ax)/x
A
a
18
Q
lim x–>0 sin(ax)/ sin(bx)
A
a/b
19
Q
Trig Identity: sin(2x)
A
=2sin(x)cos(x)
20
Q
Trig Identity: cos(2x)
A
cos²(x) -sin²(x)= 1-2sin²(x)
21
Q
Trig Identity: cos²(x)
A
(1/2)(1 + cos(2x))
22
Q
Trig Identity: sin²(x)
A
(1/2)(1 - cos(2x))
23
Q
Trig Identity: sec²(x)
A
1+ tan²(x)
24
Q
Trig Identity: csc²(x)
A
cot²(x) +1
25
∫sin²(x)
(x/2)- (1/2)sin(x)cos(x)
26
∫cos²(x)
(x/2)+ (1/2)sin(x)cos(x)
27
Trig Substitution √ ̅ (a²- x²)
x= asin(θ)
dx= acos (θ)
√ ̅ (a²- x²) = acos(θ)
28
Trig Substitution √ ̅(x²+ a²)
x= a tan(θ)
dx= asec²(θ)
√ ̅(x²+ a²)= a sec(θ)
29
Trig Substitution √ ̅(x²- a²)
x= asec(θ)
dx= asec(θ)tan(θ)
√ ̅(x²- a²)= a tan(θ)
