# lect10 - P D S C S 1 1 2 C o m p u t e r S c& E n g g I...

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Unformatted text preview: P D S : C S 1 1 2 C o m p u t e r S c & E n g g : I I T K h a r a g p u r 1 ’ & \$ % C o m p u t a t i o n o f s i n ( x ) P o w e r S e r i e s s i n x = x- x 3 3 ! + x 5 5 !- x 7 7 ! + x 9 9 ! · · · F i n i t e n u m b e r o f t e r m s o f t h i s i n fi n i t e s e r i e s m a y b e u s e d t o c o m p u t e a n a p p r o x i m a t e v a l u e o f s i n ( x ) , w h e r e x i s i n r a d i a n . L e c t 1 G o u t a m B i s w a s P D S : C S 1 1 2 C o m p u t e r S c & E n g g : I I T K h a r a g p u r 2 ’ & \$ % s i n x = x- x 3 3 ! + x 5 5 !- x 7 7 ! + x 9 9 ! · · · = X i ≥ (- 1 ) i x 2 i + 1 ( 2 i + 1 ) ! = X i ≥ t i , w h e r e t i = (- 1 ) i x 2 i + 1 ( 2 i + 1 ) ! L e c t 1 G o u t a m B i s w a s P D S : C S 1 1 2 C o m p u t e r S c & E n g g : I I T K h a r a g p u r 3 ’ & \$ % I n d u c t i v e D e fi n i t i o n o f t i t i =          x i f x = ,- t i- 1 x 2 2 i ( 2 i + 1 ) i f i > . T h i s i s a l s o c a l l e d r e c u r r e n c e r e l a t i o n o r r e c u r s i v e d e fi n i t i o n . L e c t 1 G o u t a m B i s w a s P D S : C S 1 1 2 C o m p u t e r S c & E n g g : I I T K h a r a g p u r 4 ’ & \$ % A p p r o x i m a t i o n o f s i n ( x ) T h e s u m u p t o t h e n t h t e r m ( S n ) o f t h e s e r i e s g i v e s a...
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## This note was uploaded on 08/29/2010 for the course CSE CS1001 taught by Professor Gb during the Fall '07 term at Indian Institute of Technology, Kharagpur.

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lect10 - P D S C S 1 1 2 C o m p u t e r S c& E n g g I...

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