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Trig functions
Trig functions, formulas, rules, derivatives, and anti derivatives.
22
Mathematics
Undergraduate 2
02/08/2010
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Term
cos^2(x)+sin^2(x)
 Definition
1
Term
cos(a+b)
 Definition
cos(a)cos(b)+sin(a)sin(b)
Term
sin'(x)
 Definition
cos(x)
Term
cos'(x)
 Definition
-sin(x)
Term
cos^2(x)
(half angle)
 Definition
(1+cos(2x))/2
Term
sin^2(x)
(half angle)
 Definition
(1-cos(x))/2
Term
1+tan^2(x)
 Definition
sec^2(x)
Term
cot^2(x)+1
 Definition
csc^2(x)
Term
sqrt(x^2-x^2*sin^2(theta))
 Definition
x*cos(theta)
Term
sqrt(x^2+x^2tan^2(theta))
 Definition
x*sec^2(theta)
Term
tan'(x)
 Definition
sec^2(x)
Term
sec'(x)
 Definition
sec(x)tan(x)
Term
integrate[sec(x)]
 Definition
ln|sec(x)+tan(x)|
Term
integrate[1/x dx]
 Definition
ln(x)
Term
ln(e^x)
 Definition
x
Term
Value of improper integral is a finite number
 Definition
Converge
Term
Improper integral goes to infinite
 Definition
Diverges
Term
name the types of improper integrals
 Definition
Type I: infinite bounds
Type II: has an asymptote
Term
when does the integral from 0 to inf (1/x^p) diverge and converge
 Definition

diverges when p<1

converges when p>1
Term
when does the integral from 0 to 1 (1/x^p) diverge and converge
 Definition
diverges when p>1
converges when p<1
Term
How does direct comparison work if function A<=B?
 Definition

If B equals a constant, then A equals a constant, and both A and B converge

If A goes to inf, then B goes to inf, and both A and B diverge
Term
Explain limit comparison if A<=B
 Definition

lim     A/B=L

(x->inf)             

L tells if they both converge or diverge
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