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• Asymptote (geometry)
  ...the vertical asymptotes of 1) <math>y = \frac{1}{x^2-5x}</math> 2) <math>\tan 3x</math>. 2) Since <math>\tan 3x = \frac{\sin 3x}{\cos 3x}</math>, we need to find where <math>\cos 3x =
  4 KB (664 words) - 11:44, 8 May 2020
• Mock AIME 3 Pre 2005 Problems
  The value of <math>\tan\left(\Omega\right)</math> can be expressed as <math>\frac{m}{n}</math>, whe
  7 KB (1,135 words) - 23:53, 24 March 2019
• Mock AIME 3 Pre 2005 Problems/Problem 15
  The value of <math>\tan\left(\Omega\right)</math> can be expressed as <math>\frac{m}{n}</math>, whe ...ric substitution; namely, define <math>\theta</math> such that <math> x = \tan{\theta}</math>. Then the RHS becomes
  2 KB (312 words) - 10:38, 4 April 2012
• 1960 IMO Problems/Problem 3
  \tan{\alpha}=\frac{4nh}{(n^2-1)a}. ...c}{b}\cdot\frac{n-1}{n+1}</math>, and <math>\text{slope}</math><math>(QA)=\tan{\angle QAB}=\frac{c}{b}\cdot\frac{n+1}{n-1}</math>.
  3 KB (501 words) - 00:14, 17 May 2015
• 1960 IMO Problems
  \tan{\alpha}=\frac{4nh}{(n^2-1)a}.
  3 KB (511 words) - 21:21, 20 August 2020
• 2007 AIME I Problems/Problem 9
  ...{1 - \cos \theta}{1 + \cos \theta}}</math>). We see that <math>\frac rx = \tan \frac{180 - \theta}{2} = \sqrt{\frac{1 - \cos (180 - \theta)}{1 + \cos (180 ...We see that <math>\frac rx = \tan \left(\frac{180 - 2\theta}{2}\right) = \tan (90 - \theta)</math>. In terms of <math>r</math>, we find that <math>x = \f
  11 KB (1,851 words) - 12:31, 21 December 2021
• 2007 AIME I Problems/Problem 12
  ...th>[\triangle EFB'] = \frac{1}{2} (FB' \cdot EF) = \frac{1}{2} (FB') (FB' \tan 75^{\circ})</math>. With some horrendous [[algebra]], we can calculate [\triangle EFB'] &= \frac{1}{2}\tan (30 + 45) \cdot (20 - 5\sqrt{2} - 5\sqrt{6})^2 \\
  10 KB (1,458 words) - 20:50, 3 November 2023
• 2007 AIME II Problems/Problem 15
  ...2}{3}</math> according to half angle formula. Similarly, we can find <math>tan\angle NCK=\frac{1}{2}</math>. So we can see that <math>JK=ON=14-\frac{7x}{2
  11 KB (2,099 words) - 17:51, 4 January 2024
• 1961 IMO Problems/Problem 5
  <math>b \tan{\frac{\omega}{2}} \le c < b</math> ...we require <math>AX \geqslant AC > AB</math>. But <math>\frac{AB}{AX} = \tan{\frac{\omega}{2}}</math>, so we get the condition in the question
  1 KB (205 words) - 04:12, 7 June 2021
• LaTeX:Commands
  ...||\cos||<math>\textstyle \sin</math>||\sin||<math>\textstyle \tan</math>||\tan
  12 KB (1,898 words) - 15:31, 22 February 2024
• 2006 AIME II Problems/Problem 6
  ...Also note that <cmath>AB = 1 = \overline{AA'} + \overline{A'B} = \frac{x}{\tan(15)} + x</cmath> Using the fact <math>\tan(15) = 2-\sqrt{3}</math>, this yields <cmath>x = \frac{1}{3+\sqrt{3}} = \fra
  7 KB (1,067 words) - 12:23, 8 April 2024
• 1961 IMO Problems
  <math>b \tan{\frac{\omega}{2}} \le c < b</math>
  3 KB (425 words) - 21:18, 20 August 2020
• 2004 AMC 12A Problems/Problem 18
  ...e CGF</math>. Thus, <math>\angle EGF=\angle FCG</math> and <math>\tan EGF=\tan FCG=\frac{1}{2}</math>. Solving <math>EF=\frac{1}{2}</math>. Adding, the an
  5 KB (738 words) - 13:11, 27 March 2023
• 2004 AMC 10A Problems/Problem 20
  E = (0,Tan(15)); F = (1 - Tan(15),1);
  4 KB (710 words) - 02:47, 18 April 2024
• 1999 AHSME Problems
  ...al number such that <math>\sec x - \tan x = 2</math>. Then <math>\sec x + \tan x =</math>
  13 KB (1,945 words) - 18:28, 19 June 2023
• 1960 IMO Problems/Problem 6
  <cmath>\tan\left(\frac{\theta}{2}\right) = \frac{1}{x} = \frac{\sqrt{2}}{4}</cmath> ...3</math> and <math>V_1 = \frac{\pi a^2 \times H_1 H_2}{3} = \frac{\pi a^3 \tan (\angle A_1 A H_1) }{3}</math> .
  7 KB (1,214 words) - 18:49, 29 January 2018
• 1992 USAMO Problems/Problem 2
  Consider the points <math>M_k = (1, \tan k^\circ)</math> in the coordinate plane with origin <math>O=(0,0)</math>, f ...hen the left hand side of the equation simplifies to <math>\tan 89-\tan 0=\tan 89=\frac{\sin 89}{\cos 89}=\frac{\cos 1}{\sin 1}</math> as desired.
  4 KB (628 words) - 07:41, 19 July 2016
• 2000 AMC 12 Problems/Problem 17
  <math>\text {(A)}\ \sec^2 \theta - \tan \theta \qquad \text {(B)}\ \frac 12 \qquad \text {(C)}\ \frac{\cos^2 \theta ...<cmath> \frac{OB}{OC} = \frac{AB}{AC} \Longrightarrow AC \sec \theta = OC \tan \theta </cmath> We multiply both sides by <math>\cos \theta</math> to simpl
  6 KB (979 words) - 12:50, 17 July 2022
• Construction
  21. Construct <math>sin C, cos C, tan C</math> given unit segment <math>1</math> and acute angle <math>C</math>.
  3 KB (443 words) - 20:52, 28 August 2014
• 1995 USAMO Problems
  ..., </math> <math>\tan, \; \sin^{-1}, \; \cos^{-1}, \,</math> and <math>\, \tan^{-1} \,</math> buttons. The display initially shows 0. Given any positive
  3 KB (540 words) - 13:31, 4 July 2013

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