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• 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
• 2004 AMC 12B Problems/Problem 24
  ...of <math>\tan \angle CBE</math>, <math>\tan \angle DBE</math>, and <math>\tan \angle ABE</math> form a [[geometric progression]], and the values of <math ...a)\tan(DBE + \alpha) = \frac {\tan^2 DBE - \tan^2 \alpha}{1 - \tan ^2 DBE \tan^2 \alpha},
  2 KB (302 words) - 19:59, 3 July 2013
• 1995 USAMO Problems/Problem 2
  ..., </math> <math>\tan, \; \sin^{-1}, \; \cos^{-1}, \,</math> and <math>\, \tan^{-1} \,</math> buttons. The display initially shows 0. Given any positive <cmath> \cos \tan^{-1} \sqrt{(n-m)/m} = \sqrt{m/n} . </cmath>
  3 KB (516 words) - 00:18, 6 April 2020
• 2008 AMC 12A Problems
  ...midpoint of <math>BC</math>. What is the largest possible value of <math>\tan{\angle BAD}</math>?
  13 KB (2,025 words) - 13:56, 2 February 2021
• 2008 AMC 12A Problems/Problem 24
  ...dpoint]] of <math>BC</math>. What is the largest possible value of <math>\tan{\angle BAD}</math>? ..., and since <math>\tan\angle BAF = \frac{2\sqrt{3}}{x-2}</math> and <math>\tan\angle DAE = \frac{\sqrt{3}}{x-1}</math>, we have
  3 KB (513 words) - 14:35, 7 June 2018
• 2008 AMC 12B Problems/Problem 24
  ...a</math> with the x-axis and passes through the origin has equation <math>\tan(\theta)x</math>, so the line through <math>A_0</math> and <math>B_1</math>
  9 KB (1,482 words) - 13:52, 4 April 2024
• 2008 AIME I Problems/Problem 8
  Since we are dealing with acute angles, <math>\tan(\arctan{a}) = a</math>. Note that <math>\tan(\arctan{a} + \arctan{b}) = \dfrac{a + b}{1 - ab}</math>, by tangent additio
  3 KB (490 words) - 22:36, 28 November 2023
• 2008 AIME II Problems/Problem 5
  <cmath>\begin{align*}\tan{37}\times (1008-x) &= \tan{53} \times x\\ \frac{(1008-x)}{x} &= \frac{\tan{53}}{\tan{37}} = \frac{\sin{53}}{\cos{53}} \times\frac{\sin{37}}{\cos{37}}\end{align*
  8 KB (1,338 words) - 23:15, 28 November 2023
• 2008 AIME II Problems/Problem 11
  ...om the [[trigonometric identity|half-angle identity]], we find that <math>\tan(\theta) = \frac {3}{4}</math>. Therefore, <math>XC = \frac {64}{3}</math>. ...now drop altitude AY to solve for tan2A ; now since we know tan2A we know tan A = r/x in terms of r hence solve the resulting equation in r
  6 KB (1,065 words) - 20:12, 9 August 2022
• 2008 AIME II Problems/Problem 14
  ...tarrow (2-\sqrt{3}k)\cos x\le k\sin x\rightarrow \frac{2-\sqrt{3}k}{k}\le \tan x,</cmath>
  8 KB (1,387 words) - 11:56, 29 January 2024
• 2008 AMC 10B Problems/Problem 24
  <cmath>\cot(\theta)=\tan(5^\circ)</cmath>
  12 KB (1,944 words) - 17:15, 20 January 2024

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