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• 2021 AMC 12B Problems/Problem 15
  == Video Solution by OmegaLearn (Extending Lines, Angle Chasing, Trig Area) == ...er_spindle , and can be used to demonstrate that <math>3</math> colors are not sufficient to color all of the points in the plane such that points that ar
  4 KB (537 words) - 13:49, 25 February 2024
• 2021 AMC 12B Problems/Problem 24
  ...m,n,</math> and <math>p</math> are positive integers and <math>p</math> is not divisible by the square of any prime. What is <math>m+n+p?</math> ==Solution 2 (Trig) ==
  8 KB (1,279 words) - 12:07, 28 October 2023
• Ceva's theorem
  (Note that the cevians do not necessarily lie within the triangle, although they do in this diagram.) The proof using [[Routh's Theorem]] is extremely trivial, so we will not include it.
  5 KB (934 words) - 13:06, 20 February 2024
• 2022 AMC 12B Problems/Problem 24
  ...\sin^4 \frac{2 \pi}{7} + 7 \cdot 2^4 \sin^4 \frac{3 \pi}{7}</math>. Using trig we get ...as]], and the desired identity follows. See [[Roots of unity]] if you have not seen this technique.
  21 KB (3,265 words) - 17:06, 15 November 2023
• 2022 AMC 12B Problems/Problem 25
  ...th>, <math>n</math>, and <math>p</math> are integers and <math>n</math> is not divisible by the square of any prime. ...circ)</math> is by memory, but we can cleverly calculate it using a common trig identity:
  20 KB (2,980 words) - 18:17, 2 January 2024
• 2023 AMC 12A Problems/Problem 15
  ...th that is <math>120</math> meters? (This figure is not drawn to scale. Do not assume that he zigzag path has exactly four segments as shown; there could ...right triangles (including <math>\triangle{RSC}</math>) will have the same trig ratios. By proportion, the hypotenuse <math>AP</math> is <math>\frac{x}{100
  7 KB (1,074 words) - 21:22, 20 November 2023

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