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Unformatted text preview: θ = cos( π/ 2θ ) cos θ = sin( π/ 2θ ) tan θ = cot( π/ 2θ ) cot θ = tan( π/ 2θ ) sec θ = csc( π/ 2θ ) csc θ = sec( π/ 2θ ) Notice that d ( π/ 2θ ) =dθ . This has the following consequence: In any integration or diﬀerentiation formula involving trigonometric functions of θ alone, we can replace all trigonometric functions by their cofunctions and change the overall sign. The use of this rule cut memorization in half. For example, Z cot θ dθ = Z cos θ dθ sin θ = ln  sin θ  + C , so Z tan θ dθ =ln  cos θ  + C . If we remember that Z sec θ dθ = ln  sec θ + tan θ  + C , then we automatically have Z csc θ dθ =ln  csc θ + cot θ  + C . And if we remember that d sec θ = sec θ tan θ dθ , then we know that d csc θ =csc θ cot θ dθ ....
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This note was uploaded on 02/12/2008 for the course MATH 104 taught by Professor Nelson during the Fall '07 term at Princeton.
 Fall '07
 Nelson
 Integration By Substitution

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