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• 2011 AIME II Problems/Problem 8
  ...the real parts of the blue dots is easily seen to be <math>8+16\cos\frac{\pi}{6}=8+8\sqrt{3}</math> and the negative of the sum of the imaginary parts o Note that <math>\sin(x) = \sin(x + \pi/2 - \pi/2) = \cos(x + \pi/2)</math>.
  5 KB (805 words) - 18:46, 27 January 2024
• 2011 AMC 10B Problems
  ...o went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and ...integers <math>a</math> and <math>b</math>, Ron reversed the digits of the two-digit number <math>a</math>. His erroneous product was <math>161</math>. Wh
  13 KB (2,090 words) - 18:05, 7 January 2021
• 2003 AMC 10B Problems
  ...l, and Al's pills cost a total of <math> \ </math><math>546</math> for the two weeks. How much does one green pill cost? ...math>. What is the distance between the <math>x</math>-intercepts of these two lines?
  15 KB (2,166 words) - 21:17, 16 February 2021
• 2007 AMC 10B Problems
  ...nd <math>1.5</math> points for each problem left unanswered. After looking over the <math>25</math> problems, Sarah has decided to attempt the first <math> Two points <math>B</math> and <math>C</math> are in a plane. Let <math>S</math>
  15 KB (2,297 words) - 12:57, 19 February 2020
• 2007 AMC 10B Problems/Problem 13
  ...(0,2).</math> What is the area of the intersection of the interiors of the two circles? ...\frac{\pi \sqrt{3}}{3} \qquad\textbf{(D) } 2(\pi -2) \qquad\textbf{(E) } \pi</math>
  898 bytes (142 words) - 20:42, 15 February 2024
• 1998 AHSME Problems/Problem 16
  The figure shown is the union of a circle and two semicircles of diameters <math>a</math> and <math>b</math>, all of whose ce The area of the whole circle is <math>A_{big} = \pi\cdot (a + b)^2</math>
  2 KB (307 words) - 18:58, 11 January 2014
• Area of an equilateral triangle
  ''Method 1:'' Dropping the altitude of our triangle splits it into two triangles. By HL congruence, these are congruent, so the "short side" is <m ...ac{ab\sin{C}}{2}</math>. Plugging in <math>a=b=s</math> and <math>C=\frac{\pi}{3}</math> (the angle at each vertex, in radians), we get the area to be <m
  1 KB (189 words) - 04:06, 18 June 2018
• Trigonometric Equations
  Solve for <math>x</math> for all answers in the domain <math>[0, 2\pi]</math>. We have a problem! The domain for values of <math>x</math> is <math>[0, 2\pi]</math>. However, no real value of <math>x</math> can become imaginary when
  8 KB (1,351 words) - 20:30, 10 July 2016
• 2012 AMC 12B Problems/Problem 23
  ...with <math>|z_0|=1.</math> What is the sum of all values <math>P(1)</math> over all the polynomials with these properties? ...these cases, <math>P(-1)=4-4+t-t+0=0</math>. The sum of <math>P(1)</math> over these cases is <math>\sum_{t=0}^{4} (4+4+t+t) = 40+20=60</math>.
  11 KB (1,979 words) - 17:25, 6 September 2021
• 1967 AHSME Problems
  The difference in the areas of two similar triangles is <math>18</math> square feet, and the ratio of the larg <math>\textbf{(A)}\ \frac{\pi m^2}{2}\qquad
  20 KB (3,108 words) - 14:14, 20 February 2020
• Interior angle
  The '''interior angle''' is the [[angle]] between two line segments, having two endpoints connected via a path, facing the path connecting them. ...erior angles of an <math>n</math> sided regular polygon,are <math>180(1-{2\over n})</math> degrees.
  673 bytes (105 words) - 22:28, 27 February 2020
• 2003 AMC 10B Problems/Problem 19
  ...qquad\textbf{(D) } \frac{\pi +\sqrt{3}}{2} \qquad\textbf{(E) } \frac{7}{6}\pi - \frac{\sqrt{3}}{2}</math> ...n into <math>\frac{5}{6}</math> of a circle with radius <math>1</math> and two equilateral triangles with side length <math>1</math>.
  4 KB (606 words) - 13:19, 9 July 2021
• 1984 AHSME Problems/Problem 15
  This looks a lot like the formula relating the slopes of two [[perpendicular]] [[Line|lines]], which is <math> m_1\times m_2=-1 </math>, ...> 2x+3x=5x </math>, so <math> 5x=\frac{\pi}{2} </math> and <math> x=\frac{\pi}{10} </math>, or <math> 18^\circ, \boxed{\text{A}} </math>.
  3 KB (493 words) - 18:16, 4 June 2021
• 2009 AMC 8 Problems
  ...mbered sectors. What is the probability that the sum of the numbers in the two sectors is prime? draw((0,0)--(cos(pi/6),sin(pi/6)));
  18 KB (2,548 words) - 18:03, 22 June 2024
• 2000 AMC 8 Problems/Problem 19
  ...\ 10+5\pi\qquad\text{(C)}\ 50\qquad\text{(D)}\ 50+5\pi\qquad\text{(E)}\ 25\pi </math> Draw two squares: one that has opposing corners at <math>A</math> and <math>B</math
  2 KB (383 words) - 16:58, 12 January 2024
• 1995 AJHSME Problems/Problem 9
  ...angle. But <math>24</math> is too low, as it is less than the area of the two circles. Thus, the only reasonable answer is <math>\boxed{C}</math>, which
  2 KB (409 words) - 00:15, 5 July 2013
• 2008 AMC 8 Problems/Problem 18
  Two circles that share the same center have radii <math>10</math> meters and <m ...extbf{(C)}\ 10\pi+40\qquad\textbf{(D)}\ 20\pi+20\qquad \\ \textbf{(E)}\ 20\pi+40</math>
  2 KB (210 words) - 13:37, 19 October 2020
• 2010 AMC 8 Problems/Problem 23
  ...the center <math>O</math>. What is the ratio of the combined areas of the two semicircles to the area of circle <math>O</math>? ...ac{\sqrt 2}{4}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{\pi}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{\sqrt 2}{2} </math
  2 KB (298 words) - 00:29, 18 December 2023
• 2009 AMC 8 Problems/Problem 12
  ...mbered sectors. What is the probability that the sum of the numbers in the two sectors is prime? draw((0,0)--(cos(pi/6),sin(pi/6)));
  1 KB (179 words) - 19:36, 15 April 2023
• 1979 USAMO Problems/Problem 4
  There are two ways to solve this problem. The first is more subtle, and the second is jus ...ngle POR,</math> and <math>b = \angle POQ.</math> Then <math>\angle ORP = \pi - x - a</math> and <math>\angle OQP = x - b.</math> Using the Law of Sines
  3 KB (568 words) - 12:24, 11 March 2018

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