Use Newton's method to solve the equation sec x = 4 in the interval x in (0, pi/2).

Question

In other words, use Newton's Method to compute arcsec(4).
(You need to make a good initial guess for the root otherwise Newton's method will probably fail. Please justify how you came up with your initial guess. Stop the iteration process
when you are correct to 4 decimal places.)

Answer 1

You need to be doing this on your calculator.

I will start you.
x=75 deg
sec75=3.36
try higher
sec 78=4.8 lower
sec 76.5=4.28 lower
sec 76=4.13 lower
sec 75.5=3.99 higher
sec 75.51=3.9966 higher
sec 75.515=3.99797 higher
sec 75.52=3.9993
sec 75.525=4.00067 lower
sec 75.524=4.0004
sec 75.523=4.0001
sec 75.5228=4.00008
sec 75.5223=3.99995=
sec 75.5225=4.000003
with practice, you get pretty good.

Answer 2

thanks but i need to use newton's method for this.... i tried it by starting with 1 but do not get an answer. :s