Question

Use Newton's method to determine the angle θ, between 0 and π/2 accurate to six decimal places. for which sin(θ) = 0.1. Show your work until you start computing x1, etc. Then just write down what your calculator gives you.

Answer 1

Answer:

x3=0.100167

Explanation:

Let's find the answer.

Because we are going to find the solution for sin(Ф)=0.1 then:

f(x)=sin(Ф)-0.1 and:

f'(x)=cos(Ф)

Because 0<Ф<π/2 let's start with an initial guess of 0.001 (x0), so:

x1=x0-f(x0)/f'(0)

x1=0.001-(sin(0.001)-0.1)/cos(0.001)

x1= 0.100000

x2=0.100000-(sin(0.100000)-0.1)/cos(0.100000)

x2=0.100167

x3=0.100167