This preview shows page 1. Sign up to view the full content.
Unformatted text preview: θ = cos( π/ 2-θ ) cos θ = sin( π/ 2-θ ) tan θ = cot( π/ 2-θ ) cot θ = tan( π/ 2-θ ) sec θ = csc( π/ 2-θ ) csc θ = sec( π/ 2-θ ) Notice that d ( π/ 2-θ ) =-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 ....
View Full Document
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
- Integration By Substitution