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ECE
190
Midterm Exam
1
Spring 2011
Monday, February 14, 2011
In this assignment, you will need to write a program to compute the arcsine function using the Newton-Raphson method.
Arcsine takes as input a number between -1 and 1 and returns a number between
−
!
!
and
!
!
such that the sine of the
arcsine of
x
is
x
; in other words, arcsine is the functional inverse of sine.
To find arcsine of
y
, we will find a root of
!
!
=
sin
(
!
)
−
!
; that is, we will find a point at which
sin
(
!
)
−
!
=
0
. You MUST use this approach. We start with a guess
!
!
and iterate such that new guess is
!
!
!
!
=
!
!
−
!
(
!
!
)
!
!
(
!
!
)
Remember that
!
!
!
=
sin
(
!
!
)
−
!
and
!
!
!
!
=
cos
(
!
!
)
.
Your program must start by reading two floating point numbers from the user.
The first input will be
y
and the second
input will be your initial guess for
!
!
. After each iteration, you should print "
Next iteration:
" followed by the
new value of
!
!

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## This note was uploaded on 03/08/2012 for the course ECE 190 taught by Professor Hutchinson during the Spring '08 term at University of Illinois, Urbana Champaign.

- Spring '08
- Hutchinson