What is taylor cos(θ) ?

The answer to taylor cos(θ) is sum from n=0 to infinity}(-1)^n(x^{2n of)/((2n)!)

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taylor cos(θ)

taylor

cos (θ)

n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n}}{( 2 n ) !}

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d θ} ( cos ( θ ) ) ( 0 )}{1 !} θ + \frac{\frac{d ^{2}}{d θ ^{2}} ( cos ( θ ) ) ( 0 )}{2 !} θ^{2} + \frac{\frac{d ^{3}}{d θ ^{3}} ( cos ( θ ) ) ( 0 )}{3 !} θ^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} θ + \frac{- 1}{2 !} θ^{2} + \frac{0}{3 !} θ^{3} + \frac{1}{4 !} θ^{4} + \frac{0}{5 !} θ^{5} + \frac{- 1}{6 !} θ^{6} + \frac{0}{7 !} θ^{7} + \frac{1}{8 !} θ^{8} + \dots

Refine

= 1 - \frac{1}{2 !} θ^{2} + \frac{1}{4 !} θ^{4} - \frac{1}{6 !} θ^{6} + \frac{1}{8 !} θ^{8} + \dots

The series sum representation

= n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n}}{( 2 n ) !}

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What is taylor cos(θ) ?
The answer to taylor cos(θ) is sum from n=0 to infinity}(-1)^n(x^{2n of)/((2n)!)