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.

Question

Engineering

Kendall Cook

22 May, 07:35

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.

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Answers (1)

Know the Answer?

Savanna Ellis · Answer 1

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