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Sine powered sum (Posted on 2025-05-02)

Find sin⁴(π/45) + sin⁴(2π/45) + ... + sin⁴(89π/45).

No Solution Yet Submitted by Danish Ahmed Khan

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Estimate and Brute force

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According to Wolfram Alpha, the the integral of sin^4(x) from 0 to 2π is 3*π/4. This means the average value over that domain is (3*π/4)/(2π) = 3/8.

If there are 89 addends with average value 3/8, multiply and get 267/8 = 33.375

If we made it 90 instead of 89: 270/8 = 33.75

A brute force program finds 33.75000000000002

Posted by Larry on 2025-05-02 18:25:00

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