Question

How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

score 96 · Answer 1 · 2026-03-29 03:36:28

96

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How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

Published on 29 Mar 2026 - 3:36

score 1.4k · Answer 2 · 2018-05-18 13:36:51

1.4k

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Evaulating the trigonometric integral $\int \frac{1}{(x^2+1)^2} \, dx$

Published on 18 May 2018 - 13:36

score 29 · Answer 3 · 2018-05-18 14:07:30

Would this be a valid way of proving a trigonometric value despite one of the sides of the triangle being negative?

score 124 · Answer 4 · 2026-03-25 06:39:03

124

Views

How to explain this point transformation?

Published on 25 Mar 2026 - 6:39

score 44 · Answer 5 · 2018-05-18 16:39:47

44

Views

Locate an object by sightings from two other points.

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score 38 · Answer 6 · 2018-05-18 16:47:49

38

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General sum-to-product trigonometric formula for interfering waves?

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score 2.1k · Answer 7 · 2018-05-18 21:50:34

2.1k

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How to get the exact value of $\sin(x)$ if $\sin(2x) = \frac{24}{25}$

Published on 18 May 2018 - 21:50

score 343 · Answer 8 · 2026-03-26 22:31:25

343

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Maximizing $3\sin^2 x + 8\sin x\cos x + 9\cos^2 x$. What went wrong?

Published on 26 Mar 2026 - 22:31

score 152 · Answer 9 · 2018-05-19 05:30:03

152

Views

arctangent approximation with explicit error bound

Published on 19 May 2018 - 5:30

score 786 · Answer 10 · 2026-03-25 01:18:50

786

Views

Summation of $\sum_{r=1}^{n} \frac{\cos (2rx)}{\sin((2r+1)x \sin((2r-1)x}$

Published on 25 Mar 2026 - 1:18

score 278 · Answer 11 · 2026-03-28 21:57:00

278

Views

Evaluating $\sum_{n=1}^{N} 2^{-n}\sin(n\theta)$

Published on 28 Mar 2026 - 21:57

score 55 · Answer 12 · 2018-05-19 12:32:21

55

Views

If $t = \sec x$, solve $t^2 + t - 1 = a$ and find the range of values of $a$

Published on 19 May 2018 - 12:32

score 133 · Answer 13 · 2026-03-25 22:06:05

133

Views

Is this way of evaluating $\lim_{x\to 0}\frac{x-\sin x}{x^3}$ rigorous?

Published on 25 Mar 2026 - 22:06

score 86 · Answer 14 · 2018-05-19 15:41:23

86

Views

Why can't we simply replace the sines in the Law of Sines with cosines?

Published on 19 May 2018 - 15:41

score 513 · Answer 15 · 2018-05-19 19:55:40

513

Views

Find period of the following function

Published on 19 May 2018 - 19:55

List Question

How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

Evaulating the trigonometric integral $\int \frac{1}{(x^2+1)^2} \, dx$

Would this be a valid way of proving a trigonometric value despite one of the sides of the triangle being negative?

How to explain this point transformation?

Locate an object by sightings from two other points.

General sum-to-product trigonometric formula for interfering waves?

How to get the exact value of $\sin(x)$ if $\sin(2x) = \frac{24}{25}$

Maximizing $3\sin^2 x + 8\sin x\cos x + 9\cos^2 x$. What went wrong?

arctangent approximation with explicit error bound

Summation of $\sum_{r=1}^{n} \frac{\cos (2rx)}{\sin((2r+1)x \sin((2r-1)x}$

Evaluating $\sum_{n=1}^{N} 2^{-n}\sin(n\theta)$

If $t = \sec x$, solve $t^2 + t - 1 = a$ and find the range of values of $a$

Is this way of evaluating $\lim_{x\to 0}\frac{x-\sin x}{x^3}$ rigorous?

Why can't we simply replace the sines in the Law of Sines with cosines?

Find period of the following function

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