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• 2019 AMC 12A Problems
  ...\qquad\textbf{(D) } 10 \pi \left(\sqrt{3} - 1\right) \qquad\textbf{(E) } \pi\left(\sqrt{3} + 6\right)</math> ...d the line containing side <math>\overline{BC}</math> is tangent to <math>\gamma</math>. Segments <math>\overline{AO}</math> and <math>\overline{BC}</math>
  14 KB (2,180 words) - 06:56, 9 June 2024
• 2016 AIME I Problems/Problem 9
  markangle(Label("$\gamma$", Relative(0.5)), n=1, S, A, C); <cmath> \cos (90- \alpha) = \frac{1}{5} \implies \cos (\beta + \gamma) = \frac{1}{5}</cmath>
  9 KB (1,526 words) - 02:31, 29 December 2021
• Gmaas
  ...te dreadful. EDIT: He now eats gnats again. He thinks that they taste like pi(e). EDIT: He ate 3,141,592,653,589,793,238,462,643,383 so far. 4. Gmaas wants every fact to have a pi reference. Gmaas created pi. EDIT: He made it 3.1415926 times.
  69 KB (11,805 words) - 20:49, 18 December 2019
• 2016 USAJMO Problems/Problem 5
  ...ments <math>BC, CA, AB,</math> respectively, and let <math>\alpha, \beta, \gamma</math> denote the measures of <math>\angle CAB, \angle ABC, \angle BCA,</ma ...2} - \gamma.</math> Similarly, one can show that <math>\angle OAC = \frac{\pi}{2} - \beta.</math> (One could probably cite this as well-known, but I have
  10 KB (1,733 words) - 19:15, 14 June 2020
• 2018 AMC 12B Problems/Problem 25
  label("$\Gamma$", A, W*15); ...3</math>, the arcs inside the shaded equilateral triangle are each <math>2\pi/3</math>. Also, the distances between the centers of any two of the <math>3
  13 KB (2,080 words) - 19:09, 21 October 2023
• 2015 UNM-PNM Statewide High School Mathematics Contest II Problems
  ...\sin{2\beta} , \sin(2\gamma)</math> where <math>\alpha + \beta + \gamma = \pi.</math> Express the product <math>P = sin(\alpha) sin(\beta) sin(\gamma)</math> in terms of <math>A</math>.
  4 KB (604 words) - 03:48, 12 January 2019
• 2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7
  ...\sin{2\beta} , \sin(2\gamma)</math> where <math>\alpha + \beta + \gamma = \pi.</math> Express the product <math>P = sin(\alpha) sin(\beta) sin(\gamma)</math> in terms of <math>A</math>.
  383 bytes (58 words) - 03:53, 12 January 2019
• GMAAS
  4. The Infinity Numeral, PI, is the second deity of the Almighty Gmaas's heaven. ...te dreadful. EDIT: He now eats gnats again. He thinks that they taste like pi(e). EDIT: He ate 3,141,592,653,589,793,238,462,643,383 so far.
  85 KB (13,971 words) - 18:02, 16 May 2024
• 2021 AMC 12A Problems
  ...ft( \frac{\pi}2 \sin x\right)</math> have in the closed interval <math>[0,\pi]</math>? ...e <math>\cos \frac{2\pi}7,\cos \frac{4\pi}7,</math> and <math>\cos \frac{6\pi}7</math>, where angles are in radians. What is <math>abc</math>?
  15 KB (2,383 words) - 09:49, 25 June 2023
• 2022 AIME I Problems/Problem 15
  ...5^{\circ}}{2}</math>, <math>\beta=\frac{105^{\circ}}{2}</math>, and <math>\gamma=\frac{165^{\circ}}{2}</math>. We notice that <cmath>[(1-x)(1-y)(1-z)]^2=[\sin(2\alpha)\sin(2\beta)\sin(2\gamma)]^2=[\sin(135^{\circ})\sin(105^{\circ})\sin(165^{\circ})]^2</cmath> <cmath>
  15 KB (2,208 words) - 01:25, 1 February 2024
• Functional equation for the zeta function
  \zeta(s)=2^s\pi^{s-1}\sin\left(\pi s\over2\right)\Gamma(1-s)\zeta(1-s) B_1(x)\triangleq\{x\}-\frac12=-\sum_{n=1}^\infty{\sin(2\pi nx)\over\pi n}
  4 KB (682 words) - 03:56, 13 January 2021
• 2021 IMO Problems/Problem 3
  ...angle ACB = \gamma</math>. Then <math>\angle BXC = \angle BXE = \pi – 2\gamma,</math> <math>\angle AA'B = \gamma (AA'CB</math> is cyclic),
  7 KB (1,145 words) - 10:29, 18 June 2023
• 2021 IMO Problems/Problem 4
  Let <math>\Gamma</math> be a circle with centre <math>I</math>, and <math>ABCD</math> a conv ...segments <math>AB, BC, CD</math> and <math>DA</math> is tangent to <math>\Gamma</math>. Let <math>\Omega</math> be the circumcircle of the triangle <math>A
  7 KB (1,196 words) - 10:30, 18 June 2023
• Euler-Mascheroni constant
  ...1}{k} \right) - \ln(n) \right).</cmath> Its value is approximately <cmath>\gamma = 0.577215 \dots .</cmath> Whether <math>\gamma</math> is [[Rational number|rational]] or [[Irrational number|irrational]]
  3 KB (543 words) - 17:32, 19 September 2022
• 2022 SSMO Accuracy Round Problems
  ...volume of the region that the cone sweeps out can be expressed as <math>m\pi</math>. Find <math>m</math>. ...sum of all possible values for the number of edges (connections) in <math>\Gamma</math>.
  5 KB (830 words) - 13:04, 14 December 2023
• Know the Facts: Gmaas
  ...te dreadful. EDIT: He now eats gnats again. He thinks that they taste like pi(e). EDIT: He ate 3,141,592,653,589,793,238,462,643,383 so far. 4. Gmaas wants every fact to have a pi reference. Gmaas created pi. EDIT: He made it 3.1415926 times.
  88 KB (14,928 words) - 13:54, 29 April 2024
• Proofs of trig identities
  Notice <math>f\left(\frac{k\pi}{2}\right)=0</math>. If we let <math>\beta=0</math>: <math>\cos(2\alpha+k\pi)=\sin^2\alpha\cos^2\alpha</math>
  16 KB (2,796 words) - 13:12, 21 January 2024
• Sharygin Olympiads, the best
  <cmath>D \in \omega \implies \angle PDC = \alpha, \angle PCD = \pi - \alpha - \varphi.</cmath> <cmath>D' \in \omega' \implies \angle PD'C = \beta, \angle PCD' = \pi - \beta - \varphi.</cmath>
  29 KB (4,997 words) - 18:06, 16 May 2024
• A7456321
  ...te dreadful. EDIT: He now eats gnats again. He thinks that they taste like pi(e). EDIT: He ate 3,141,592,653,589,793,238,462,643,383 so far. 4. Gmaas wants every fact to have a pi reference. Gmaas created pi. EDIT: He made it 3.1415926 times.
  69 KB (11,826 words) - 22:33, 22 June 2024

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