Find all solutions of the equation that lie in the interval [0, π]. State each answer rounded to two decimal places. (Enter your answers as a comma-separated list.) cos(x) = x

Question

cos(x)= x

Thanks!

Answer 1

cos (x) = x

f(x) = x - cos(x)

f'(x) = 1 + sin(x)

a₁ = a₀ - f(a₀)/f'(a₀)

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a_n+1 = a_n - f(a_n)/f'(a_n)

Take a₀ as 1

a₁ = 1 - (1 - cos(1))/(1 + sin(1))

a_{2 =} a₁ - f(a₁)/f'(a₁)

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Answer 2

cos x = x

cosx - x = 0

f(x) = cos x - x

x = 0.739