Trigonometric, exponential and logarithmic functions Flashcards
What is an even function
If f(-x)=f(x)
what is an odd function
if f(-x)=-f(x)
decomposition into an even function
f(x)=1/2(f(x)+f(-x))
decomposition into an odd function
f(x)=1/2(f(x)-f(-x))
inverse function of y=f(x)
x=f^-1(y)
sin(0)
0
sin(pi)
0
sin(3pi/2)
-1
sin(2pi)
0
cos(0)
1
cos(pi/2)
-1
cos(3pi/2)
0
cos(2pi)
1
sin(pi/4)
1/rt2
sin(pi/3)
rt3/2
sin(pi/6)
1/2
cos(pi/4)
1/rt2
cos(pi/3)
1/2
cos(pi/6)
rt3/2
sin(-π )
-sin(π )
sin(pi/2-π )
cos(π )
sin(π +pi)
-sin(π )
cos(-π )
cos(π )
cos(pi/2-π )
sin(π )
cos(π +pi)
-cos(π )
sec(x)
1/cos(x)
csc(x)
1/sin(x)
cot(x)
1/tan(x)
exp(t+s)
exp(t)exp(s)
inverse of x=logb(y)
y=b^x
b^logbx
logb(b^x)
inverse of y=e^x
x=ln(y)
e^ln(x)
ln(e^x)
e^0
1
e^1
e
ln(1)
0
ln(e)
1
e^t*e^s
e^t+s
ln(ab)
ln(a)+ln(b)
e^t/e^s
e^t-s
ln(a/b)
ln(a)-ln(b)
e^t^a
e^at
ln(a^b)
bln(a)
change of base - ln(y)
ln(b)logb(y)
polar representation of x
rcos(π)
polar representation of y
rsin(π)
Eulerβs formula
z=r(cos(π)+isin(π))=re^iπ
cos(π) - complex exponential
(e^i(π)+e^-i(π))/2
sin(π) - complex exponential
(e^i(π)-e^-i(π))/2i
cosh(x)
(e^x+e^-x)/2
sinh(x)
(e^x-e^-x)/2
tanh(x)
(e^x-e^-x)/(e^x+e^-x)
sech(x)
1/cosh(x)
csch(x)
1/sinh(x)
coth(x)
1/tanh(x)
sin(a+b)
sin(a)cos(b)+cos(a)sin(b)
cos(a+b)
cos(a)cos(b)-sin(a)sin(b)
sin(a-b)
sin(a)cos(b)-cos(a)sin(b)
cos(a-b)
cos(a)cos(b)+sin(a)sin(b)
De Moivreβs - cos(nπ)+isin(nπ)
e^inπ=(e^iπ)^n=(cos(π)+isin(π))^n
cosh^2(x)-sinh^2(x)
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