Leonhard Euler was able to find the exact sum of the series in Problem 5. In 1736 he proved that
In this problem we ask you to prove this fact by evaluating the double
This gives a rotation about the origin through the angle
[Hint: If, in evaluation the integral, you encounter either of the expressions
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Calculus 8th Edition
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning