Trigonometric, exponential and logarithmic functions Flashcards
(61 cards)
1
Q
What is an even function
A
If f(-x)=f(x)
2
Q
what is an odd function
A
if f(-x)=-f(x)
3
Q
decomposition into an even function
A
f(x)=1/2(f(x)+f(-x))
4
Q
decomposition into an odd function
A
f(x)=1/2(f(x)-f(-x))
5
Q
inverse function of y=f(x)
A
x=f^-1(y)
6
Q
sin(0)
A
0
7
Q
sin(pi)
A
0
8
Q
sin(3pi/2)
A
-1
9
Q
sin(2pi)
A
0
10
Q
cos(0)
A
1
11
Q
cos(pi/2)
A
-1
12
Q
cos(3pi/2)
A
0
13
Q
cos(2pi)
A
1
14
Q
sin(pi/4)
A
1/rt2
15
Q
sin(pi/3)
A
rt3/2
16
Q
sin(pi/6)
A
1/2
17
Q
cos(pi/4)
A
1/rt2
18
Q
cos(pi/3)
A
1/2
19
Q
cos(pi/6)
A
rt3/2
20
Q
sin(-π )
A
-sin(π )
21
Q
sin(pi/2-π )
A
cos(π )
22
Q
sin(π +pi)
A
-sin(π )
23
Q
cos(-π )
A
cos(π )
24
Q
cos(pi/2-π )
A
sin(π )
25
cos(π +pi)
-cos(π )
26
sec(x)
1/cos(x)
27
csc(x)
1/sin(x)
28
cot(x)
1/tan(x)
29
exp(t+s)
exp(t)exp(s)
30
inverse of x=logb(y)
y=b^x
31
b^logbx
logb(b^x)
32
inverse of y=e^x
x=ln(y)
33
e^ln(x)
ln(e^x)
34
e^0
1
35
e^1
e
36
ln(1)
0
37
ln(e)
1
38
e^t*e^s
e^t+s
39
ln(ab)
ln(a)+ln(b)
40
e^t/e^s
e^t-s
41
ln(a/b)
ln(a)-ln(b)
42
e^t^a
e^at
43
ln(a^b)
bln(a)
44
change of base - ln(y)
ln(b)logb(y)
45
polar representation of x
rcos(π)
46
polar representation of y
rsin(π)
47
Euler's formula
z=r(cos(π)+isin(π))=re^iπ
48
cos(π) - complex exponential
(e^i(π)+e^-i(π))/2
49
sin(π) - complex exponential
(e^i(π)-e^-i(π))/2i
50
cosh(x)
(e^x+e^-x)/2
51
sinh(x)
(e^x-e^-x)/2
52
tanh(x)
(e^x-e^-x)/(e^x+e^-x)
53
sech(x)
1/cosh(x)
54
csch(x)
1/sinh(x)
55
coth(x)
1/tanh(x)
56
sin(a+b)
sin(a)cos(b)+cos(a)sin(b)
57
cos(a+b)
cos(a)cos(b)-sin(a)sin(b)
58
sin(a-b)
sin(a)cos(b)-cos(a)sin(b)
59
cos(a-b)
cos(a)cos(b)+sin(a)sin(b)
60
De Moivre's - cos(nπ)+isin(nπ)
e^inπ=(e^iπ)^n=(cos(π)+isin(π))^n
61
cosh^2(x)-sinh^2(x)
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