Trig, Unnecessary Flashcards
(23 cards)
1
Q
sinh and cosh identity(ies)
A
coshx+sinhx=e^x coshx-sinhx=e^(-x) cosh²x-sinh²x=1
2
Q
sech and tanh identity(ies)
A
sech²x+tanh²x=1
3
Q
csch and coth identity(ies)
A
csch²x=coth²x-1
4
Q
sinh⁻¹x
A
ln( x+√(x²+1) )
5
Q
cosh⁻¹x
A
ln( x+√(x²-1) )
6
Q
d/dx tanh x
A
sech²x
7
Q
d/dx csch x
A
-csch(x) coth(x)
8
Q
d/dx sech x
A
-sech(x) tanh(x)
9
Q
d/dx coth x
A
-csch²x
10
Q
d/dx tanh x
A
sech²x
11
Q
∫tanhu du
A
ln coshu + C
12
Q
∫coshu du
A
sinhu + C
13
Q
d/dx sinh x
A
cosh x
14
Q
d/dx cosh x
A
sinh x
15
Q
∫sinhu du
A
coshu + C
16
Q
∫ sinx dx
A
-cosx + C
17
Q
∫ secx tanx dx
A
secx + C
18
Q
∫ cosx dx
A
sinx + C
19
Q
∫ csc²x dx
A
-cotx + C
20
Q
∫ tanx dx
A
ln|secx|+C
21
Q
∫ secx dx
A
ln|secx + tanx| + C
22
Q
sinhx
A
( e^x - e^(-x) ) / 2
23
Q
coshx
A
( e^x + e^(-x) ) / 2
