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• 1953 AHSME Problems/Problem 50
  ...rac{2}{3}</math>, <math>\tan{\frac{B}{2}} = \frac{1}{2}</math>, and <math>\tan{\frac{C}{2}} = \frac{4}{x},</math> so we have the equation <math>\frac{1}{2
  2 KB (314 words) - 21:17, 31 December 2023
• 2013 AMC 12B Problems
  ..., Q=(\cot x, \cot^2 x), R=(\sin x, \sin^2 x)</math> and <math>S =(\tan x, \tan^2 x)</math> are the vertices of a trapezoid. What is <math>\sin(2x)</math>?
  16 KB (2,459 words) - 02:46, 30 January 2021
• 2013 AMC 12B Problems/Problem 20
  ..., Q=(\cot x, \cot^2 x), R=(\sin x, \sin^2 x)</math> and <math>S =(\tan x, \tan^2 x)</math> are the vertices of a trapezoid. What is <math>\sin(2x)</math>? Let <math>f,g,h,j</math> be <math>\sin, \cos, \tan, \cot</math> (not respectively). Then we have four points <math>(f,f^2),(g,
  2 KB (375 words) - 00:54, 28 September 2021
• 1982 USAMO Problems/Problem 3
  ...} \cdot \frac{r}{s-b} \cdot \frac{r}{s-c} = \frac{1}{4} \tan A/2 \tan B/2 \tan C/2.</cmath> Lemma. <math>\tan x \tan (A - x)</math> is increasing on <math>0 < x < \frac{A}{2}</math>, where <ma
  2 KB (376 words) - 23:29, 18 May 2015
• 2013 AIME I Problems/Problem 14
  ...tter. Only the numerator, because we are trying to find <math>\frac{P}{Q}=\tan\text{arg}(\Sigma)</math> a PROPORTION of values. So denominators would canc
  10 KB (1,641 words) - 20:03, 3 January 2024
• 1991 AHSME Problems
  \textbf{(C) } \tan^2\theta\qquad
  16 KB (2,451 words) - 04:27, 6 September 2021
• 2003 AMC 12B Problems/Problem 10
  real r = 5/dir(54).x, h = 5 tan(54*pi/180);
  1 KB (237 words) - 23:06, 3 February 2020
• Hyperbolic trig functions
  <math>\tanh(x)= -1\tan{iz}</math>
  423 bytes (78 words) - 23:33, 22 May 2013
• 2013 USAJMO Problems/Problem 5
  <cmath>\frac{XC}{CY}=\tan {\angle CYZ}=\tan (90-\alpha)</cmath> <cmath>\frac{CQ}{CY}=\tan {\angle CYQ}=\tan (\alpha+\beta).</cmath>
  7 KB (1,250 words) - 18:05, 1 October 2021
• 2014 AIME II Problems/Problem 12
  <math>\tan{\frac{3A}{2}}\tan{\frac{3B}{2}}=1</math> Note that <math>\tan{x}=\frac{1}{\tan(90-x)}</math>, or <math>\tan{x}\tan(90-x)=1</math>
  5 KB (875 words) - 17:56, 2 October 2023
• 2013 IMO Problems/Problem 4
  ...an{\angle{C}}-1)m}{i\tan{\angle{C}}}.</cmath> We wish to simplify <math>(i\tan{\angle{C}}-1)m</math> first. Note that <cmath>m=\frac{|CM|}{|CA|}\cdot(a)=\ (i\tan{\angle{C}}-1)m&=(i\tan{\angle{C}}-1)((|BC|)\cos{\angle{C}}(\cos{\angle{C}}+i\sin{\angle{C}}))\\
  11 KB (1,991 words) - 01:31, 19 November 2023
• 2014 AMC 10A Problems/Problem 22
  ...ow EC=20-10 \sqrt 3</math>. (It is important to memorize the sin, cos, and tan values of <math>15^\circ</math> and <math>75^\circ</math>.) Therefore, we h
  13 KB (1,983 words) - 12:39, 7 June 2024
• 2014 AMC 12A Problems/Problem 25
  ...an angle <math>\theta</math> relative to the coordinate axis, where <math>\tan\theta = \tfrac 34</math>. We rotate the coordinate axis by angle <math>\the
  4 KB (661 words) - 16:18, 2 September 2022
• 2014 AMC 12B Problems/Problem 19
  ...tan {\theta})^4 - 3(\tan {\theta})^2 + 1 = 0.</math> This gives us <math>(\tan {\theta})^2 = \dfrac{3+\sqrt{5}}{2}\longrightarrow \boxed{E}</math>
  4 KB (703 words) - 16:24, 9 September 2022
• 2014 AIME I Problems
  ...\left(\tfrac{w-z}{z}\right) </math>. The maximum possible value of <math>\tan^2 \theta</math> can be written as <math>\tfrac{p}{q}</math>, where <math>p<
  9 KB (1,472 words) - 13:59, 30 November 2021
• 2014 AIME I Problems/Problem 7
  ...\left(\tfrac{w-z}{z}\right) </math>. The maximum possible value of <math>\tan^2 \theta</math> can be written as <math>\tfrac{p}{q}</math>, where <math>p< We know that <math>\tan{\theta}</math> is equal to the imaginary part of the above expression divid
  5 KB (782 words) - 20:25, 10 October 2023
• 1973 AHSME Problems
  ...nd <math> \sin \frac12 \theta = \sqrt{\frac{x-1}{2x}}</math>, then <math> \tan \theta</math> equals
  18 KB (2,788 words) - 13:55, 20 February 2020
• 1980 AHSME Problems/Problem 12
  ..._2)}{1-\tan^2(\theta_2)} = 4\tan(\theta_2)</math>. Solving, we have <math>\tan(\theta_2) = 0, \dfrac{\sqrt{2}}{2}</math>. But line <math>L_1</math> is not
  2 KB (237 words) - 18:02, 20 March 2018
• 1987 AHSME Problems
  ...c})+\log_{10}(\tan 3^{\circ})+\cdots+\log_{10}(\tan 88^{\circ})+\log_{10}(\tan 89^{\circ}). </math>
  16 KB (2,291 words) - 13:45, 19 February 2020
• 1986 AHSME Problems
  <math>\textbf{(A)}\ \tan \theta = \theta\qquad \textbf{(B)}\ \tan \theta = 2\theta\qquad
  17 KB (2,512 words) - 18:30, 12 October 2023

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