Tuesday, 14 August 2018

algebra precalculus - Evaluate this continued trigonometric sum


$$\sin^2(4) + \sin^2(8) + \sin^2(12) + ... + \sin^2(176)$$





Where the number is in degrees not radians.



$$\cos(x) = \sin(90 - x) \implies \cos(x) = \sin(90 + x)$$



$$\implies \sin(x) = \cos(x - 90)$$



$$S = \sum_{n=1}^{44} \sin^2(4n)$$

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