20BSP08finalformula

20BSP08finalformula - Formula Sheet for Final Exam Trig...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Formula Sheet for Final Exam Trig identities: sec x = 1 cos x csc x = 1 sin x cot x = cos x sin x cos 2 ( x ) = 1 + cos(2 x ) 2 sin 2 ( x ) = 1 cos(2 x ) 2 Integrals of trig functions: integraldisplay sec u du = ln | sec u +tan u | + C integraldisplay csc u du = ln | csc u cot u | + C Average value: Let f be continuous on [ a, b ]. The average value of f on [ a, b ] is f a ve = 1 b a integraldisplay b a f ( x ) dx. Area under a polar curve: Let R be the region bounded by the polar curve r = f ( ) and the rays = a and = b . Then Area R = integraldisplay b a 1 2 [ f ( )] 2 d. Complex numbers n th powers: If z = r (cos + i sin ), then for any integer n , z n = r n (cos( n ) + i sin( n )) . n th roots: For any integer n , the n th roots of r (cos + i sin ) are r 1 n parenleftbigg cos parenleftbigg + k 2 n parenrightbigg + i sin parenleftbigg + k 2 n parenrightbiggparenrightbigg , k = 0 , 1 . . ., n 1 ....
View Full Document

This note was uploaded on 06/04/2008 for the course MATH 20B taught by Professor Justin during the Spring '08 term at UCSD.

Page1 / 2

20BSP08finalformula - Formula Sheet for Final Exam Trig...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online