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Geometry Level 2

What is the value of cos ⁡ i \cos { i } correct to 3 decimal places?

Details and Assumptions

  • i i is − 1 \sqrt { -1 }

  • Consider cos ⁡ \cos as a complex valued function.


The answer is 1.543.

Aryan Gaikwad by Aryan Gaikwad , 20, India

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1 solution

Caleb Townsend
Apr 3, 2015

Use the identity cos ⁡ ( x ) = e i x + e − i x 2 \cos(x) = \frac{e^{ix} + e^{-ix}}{2} and substitute x = i x = i to obtain cos ⁡ ( x ) = e − 1 + e 1 2 = e + 1 e 2 ≈ 1.543 \cos(x) = \frac{e^{-1} + e^{1}}{2} \\ = \frac{e + \frac{1}{e}}{2} \\ \approx \boxed{1.543}

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