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• Trigonometric identities
  The plus or minus does not mean that there are two answers, but that the sign of the expression depend These are the identities that are not substantial enough to warrant a section of their own.
  8 KB (1,397 words) - 21:55, 20 January 2024
• 1983 AIME Problems/Problem 4
  ==Solution 2 (Trig)== ==Solution 4 (Trig)==
  11 KB (1,741 words) - 22:40, 23 November 2023
• 1983 AIME Problems/Problem 15
  ...intersect the chord <math>BC</math> at two points, one point, or they may not have a point of intersection. By the problem condition, however, the circle ...ave found one possible case. However, in a full-solution contest, we could not assume that the answer is unique, but would need to prove that this is the
  19 KB (3,221 words) - 01:05, 7 February 2023
• 1986 AIME Problems/Problem 3
  == Solution 3 (less trig required, use of quadratic formula) == Remark: The quadratic need not be solved. The value of <math>ab</math> can be found through Vieta's.
  3 KB (545 words) - 23:44, 12 October 2023
• 2001 AIME I Problems/Problem 4
  ...>b</math>, and <math>c</math> are positive integers, and <math>c</math> is not divisible by the square of any prime. Find <math>a+b+c</math>. ==Solution 2 (no trig)==
  3 KB (534 words) - 03:22, 23 January 2023
• 2003 AIME II Problems/Problem 14
  ...th> where <math>m</math> and <math>n</math> are positive integers and n is not divisible by the square of any prime. Find <math>m + n.</math> ==Solution 4 (No Trig)==
  9 KB (1,461 words) - 15:09, 18 August 2023
• 2005 AMC 10A Problems/Problem 25
  ==Solution 2 (no trig)== ==Solution 3 (trig)==
  6 KB (854 words) - 20:25, 24 July 2022
• 2006 AIME II Problems/Problem 12
  ...th> and <math> r</math> are [[relatively prime]], and <math> q </math> is not [[divisibility | divisible]] by the [[perfect square | square]] of any prim == Solution 3: Trig ==
  6 KB (1,033 words) - 02:36, 19 March 2022
• 2008 AMC 12B Problems/Problem 25
  Note: Once <math>DY</math> is found, there is no need to do the trig. Notice that the hexagon consists of two trapezoids, <math>ABPQ</math> and ...= X, AP \cap CD = Y.</math> Then, angle chasing shows that <math>CQ</math> not only bisects <math>BX,</math> but is also perpendicular to it. This makes i
  12 KB (2,015 words) - 20:54, 9 October 2022
• 2001 AMC 12 Problems/Problem 24
  ...irc</math> and <math>\angle ADC = 60^\circ</math> as you can see, let's do trig. Drop an altitude from <math>A</math> to <math>BC</math>; call this point < ...75^\circ</math> or <math>105^\circ</math>. Since <math>105^\circ</math> is not a choice, we know <math>\angle ACB = \boxed{75^\circ}</math>.
  8 KB (1,316 words) - 22:48, 7 March 2024
• 2009 AMC 12B Problems/Problem 24
  ...th>\sin^{-1}(\sin(6x)) = 180 - 6x</math>. As <math>\frac{180}{7}</math> is not on the interval <math>30 \leq x \leq 45</math>, this yields no solution. .... Thus, <math>\sin^{-1}(\sin(6x)) = 6x - 360</math>. As <math>72</math> is not on the interval <math>45 \leq x \leq 60</math>, this yields no solution.
  7 KB (1,287 words) - 07:09, 22 December 2022
• 2010 AMC 12A Problems/Problem 13
  ...k</math> do the graphs of <math>x^2+y^2=k^2</math> and <math>xy = k</math> not intersect? ...h of the circle. This should be enough to conclude that the hyperbola does not intersect the circle.
  9 KB (1,622 words) - 20:53, 11 September 2023
• 2010 AMC 12A Problems/Problem 24
  ...egative. Continuing the pattern and accounting for doubled roots (which do not flip sign), we realize that there are <math>5</math> negative intervals fro ...count it as two disjoint intervals. Note that this will be important as to not undercounting disjoint intervals. )
  9 KB (1,434 words) - 17:54, 17 August 2022
• Python reference
  while word[0] not in vowels: ...erything from position 1, including position 1, all the way to position 3, not including position 3. This is called a slice.
  28 KB (4,762 words) - 21:20, 12 June 2023
• 2011 AMC 10B Problems/Problem 18
  ==Solution 2 (with trig, not recommended)== ==Solution 3(Easier Trig)==
  5 KB (782 words) - 14:29, 1 April 2024
• 2002 AMC 10B Problems/Problem 24
  == Solution 2 (trig) == ...e time in seconds. Since <math>x=0</math> is at the crest of the graph and not at the midline, we will use a cosine graph. Therefore, we will use the form
  3 KB (559 words) - 02:44, 8 February 2024
• 1984 AHSME Problems/Problem 26
  ...d \mathrm{(C) \ } 15 \qquad \mathrm{(D) \ }18 \qquad \mathrm{(E) \ } \text{Not uniquely determined} </math> .../math> to get that <math>BD=\frac{c\cos{\beta}}{2}</math>. We can also use trig manipulation on <math>BCE</math> to get that <math>CE=a\tan{\beta}</math>.
  2 KB (303 words) - 20:28, 2 October 2023
• 2012 AIME I Problems/Problem 12
  ...latively prime positive integers, and <math>p</math> is a positive integer not divisible by the square of any prime. Find <math>m+n+p.</math> ...ector Theorem or the Law of Cosines, but it uses the Law of Sines and more trig)
  9 KB (1,523 words) - 12:23, 7 September 2022
• Mock Geometry AIME 2011 Problems/Problem 12
  ...</math>, where <math>a,b,c</math> are positive integers, <math>b</math> is not divisible by the square of any prime, and <math>a</math> and <math>c</math> == Solution 2 (Trig) ==
  5 KB (831 words) - 17:55, 21 July 2018
• 2013 AIME I Problems/Problem 12
  ...h>, where <math>a</math> and <math>d</math> are relatively prime, and c is not divisible by the square of any prime. Find <math>a+b+c+d</math>. ...ath>H</math>, and note that <math>QP = 1 + \sqrt{3}</math> after using the trig functions for <math>75</math> degrees.
  7 KB (1,068 words) - 12:11, 10 August 2021

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