ch17sc7and8trighyp

ch17sc7and8trighyp - - 1 2 sin ln 1 z i iz z- = -+- Math...

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

View Full Document Right Arrow Icon
1 sin 2 iz iz e e z i - - = ( ) ( ) ( ) ( ) , , sin sin cosh cos sinh u x y v x y z x y i x y = + dhhDhh± dhhDhh± Section 17.7 Trigonometric and Hyperbolic Functions ( ) ( ) 2 i x iy i x iy e e i + - + - = 2 2 ix y ix y e e e e i i - - = - ( ) ( ) cos sin cos sin 2 2 y y x i x e x i x e i i - + - = - ( ) ( ) cos sin cos sin 2 2 y y i x i x e i x i x e - - + - = + ( ) ( ) sin cos sin cos 2 2 y y x i x e x i x e - - + = + ( ) sin cos sin cos 2 y y y y e x ie x e x ie x - - - + + = sin cos 2 2 y y y y e e e e x i x - - + - = + 2 y ix y ix e e i - + - - = Math 241 – Rimmer sinh 2 z z e e z - - = ( ) ( ) sinh sinh cos cosh sin z x y i x y = + cos 2 iz iz e e z - + = ( ) ( ) ( ) ( ) , , cos cos cosh sin sinh u x y v x y z x y i x y = - dhhDhh± dhhDhh± cosh 2 z z e e z - + = ( ) ( ) cosh cosh cos sinh sin z x y i x y = + Math 241 – Rimmer 17.7 Trigonometric and Hyperbolic Functions All trig. identities of a real variable hold for trig. functions of a complex variable
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 1 sin if sin w z z w - = = iw u e = Quadratic with 1, 2 , 1 a b iz c = = - = - Section 17.8 Inverse Trigonometric Functions 2 iw iw e e z i - - = 1 2 iw iw e iz e - = 2 iw iw e e iz - - = 2 1 2 iw iw e iz e - = 2 2 1 0 iw iw e ize - - = Solve for . w 2 2 1 0 u izu - - = ( ) ( )( ) 2 2 4 2 4 1 1 b ac iz - = - - - 2 2 4 4 2 iz z u ± - = 2 4 4 z = - + ( ) 2 2 4 1 2 iz z ± - = 2 2 2 1 2 iz z ± - = 2 1 iz z = ± - 2 1 iw e iz z = + - 2 square root has two values 1 u iz z = + - 2 ln 1 w i iz z = - + - 2 ln ln 1 iw e iz z = + - 2 ln 1 iw iz z = +
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: - 1 2 sin ln 1 z i iz z- = -+- Math 241 Rimmer 1 2 cos ln 1 z i z i z- = -+- 1 5 Find cos 3- 5 3 z = 2 25 1 1 9 z-= -2 16 4 1 9 3 z i-=-= 16 9 = -1 5 5 4 cos ln 3 3 3 i- = - 2 2 4 1 3 i z i-= 2 4 1 3 i z-= 1 ln3 5 cos 1 3 ln 3 i i-- = - ( ) ( ) ln ln 2 z z i n = + + ( ) ln3 2 ln 3 i n i-=-( ) ( ) ln 3 ln 3 2 i n = + + 1 1 ln 2 ln 3 3 i n i -=- ( ) 1 1 ln ln 2 3 3 i n = + + ( ) 2 ln1 ln 3 n i =--2 ln3 n i = + 1 5 cos 2 ln 3 3 n i- =...
View Full Document

This note was uploaded on 09/27/2009 for the course ECON 101 taught by Professor Dannicatambay during the Spring '08 term at UPenn.

Page1 / 2

ch17sc7and8trighyp - - 1 2 sin ln 1 z i iz z- = -+- Math...

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