# Tagged Questions

For questions about or related to trigonometric series.

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### To compute $\tan1-\tan3+\tan5-\cdots+\tan89$, $\tan1+\tan3+\tan5+\cdots+\tan89$

How do we compute : $$i)\ S_1 = \tan1-\tan3+\tan5-\cdots+\tan89$$ and $$ii)\ S_2 = \tan1+\tan3+\tan5+\cdots+\tan89$$ all the angles are in degrees. Thanks
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### Example of a trigonometric series that is not fourier series?

My textbook doesn't give any example of this kind of series. Could you provide some? Trigonometric series is defined in wikipedia as : $A_{0}+\sum_{n=1}^{\infty}(A_{n} \cos{nx} + B_{n} \sin{nx})$ ...
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### Value of a Sine-Like Infinite Product

Does the following infinite product have a "nice" closed form? $$P = \prod_{k=2}^{\infty} \left(\left(1 - \frac{1}{k^2}\right)^\dfrac{(-1)^k}{k}\right)$$ I know that without the power one could ...
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### Evaluation of a trigonometric partial sum

I just wanted to evaluate $$\sum_{k=0}^n \cos k\theta$$ and I know that it should give $$\cos\left(\frac{n\theta}{2}\right)\frac{\sin\left(\frac{(n+1)\theta}{2}\right)}{\sin(\theta / 2)}$$ ...
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### Can we subtract a trigonometric term from a polynomial?

Can we find the root of a function like $f(x) = x^2-\cos(x)$ using accurate algebra or do we need to resort to numerical methods approximations? thanks.
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### Sum of weighted cosine functions (2)

I had written a question but I did not formulate the problem correctly (sorry). The last question is in this link. I am writing the problem again and I would appreciate any help. Assume $\theta_{ij}$ ...