The value of cos(46^∘) is known to be approximately 0.694658. Solve for the tangent line of cos(x) at x=π/4. Use the tangent line to estimate the value of cos(46^∘). cos(46∘)≈

Answer 1

f(x) = cosx; x₀ = 45° = π/4; Δx = 1° = π/180; cos46° = cos45° + Δf ≈ √2/2 + df = √2/2 - sin45°·π/180 = 0.694765