Trig Rules Flashcards
∫sec(x)tan(x)
sec(x) + C
∫csc(x) cot(x)
-csc(x) +C
∫csc²(x)
-cot(x) + C
∫tan(x)
ln| sec(x)| +C
∫sec(x)
ln |sec(x) + tan(x)| +C
∫1/(a² +x²)
1/a tan−1(x/a) +C
∫ 1/ √(a- x²)
sin−1( x/a) +C
∫ ln(x)
xln(x) -x +C
(sec(x))’
sec(x)tan(x)
(csc(x))’
-csc(x) cot(x)
(cot(x))’
-csc² (x)
∫a^x
1/ln(a)*a^x
(cos-1(x))’
-1/√(1-x²)
(tan-1(x))’
1/(1+x²)
lim x–>0 (sin(x)/x)
1
lim x–>0 (cos(x) -1)/x
0
lim x–> 0 sin(ax)/x
a
lim x–>0 sin(ax)/ sin(bx)
a/b
Trig Identity: sin(2x)
=2sin(x)cos(x)
Trig Identity: cos(2x)
cos²(x) -sin²(x)= 1-2sin²(x)
Trig Identity: cos²(x)
(1/2)(1 + cos(2x))
Trig Identity: sin²(x)
(1/2)(1 - cos(2x))
Trig Identity: sec²(x)
1+ tan²(x)
Trig Identity: csc²(x)
cot²(x) +1
∫sin²(x)
(x/2)- (1/2)sin(x)cos(x)
∫cos²(x)
(x/2)+ (1/2)sin(x)cos(x)
Trig Substitution √ ̅ (a²- x²)
x= asin(θ)
dx= acos (θ)
√ ̅ (a²- x²) = acos(θ)
Trig Substitution √ ̅(x²+ a²)
x= a tan(θ)
dx= asec²(θ)
√ ̅(x²+ a²)= a sec(θ)
Trig Substitution √ ̅(x²- a²)
x= asec(θ)
dx= asec(θ)tan(θ)
√ ̅(x²- a²)= a tan(θ)
