Question

2Cos (3/10x) - 3Sin(1/2x)=0

Answer 1

Let f(x)=2cos(0.3x)-3sin(.5x).

f'(x)=-0.6sin(0.3x)-1.5cos(0.5x).

Use Newton’s Method:

xᵢ₊₁=xᵢ-f(xᵢ)/f'(xᵢ) where xᵢ=x₀, x₁, x₂, ... are successive iterations for the solution x. Let x₀=0, then x₁=4/3, so:

x₂=1.324138581,

x₃=1.324147453,

x₄=1.324147453, which is stable, so x=1.3241 approx.