Search results

  • ...h>m</math> and <math>n</math> are positive integers, and <math>n</math> is not divisible by the square of any prime. Find <math>m+n.</math> ==Solution 1 (No trig)==
    16 KB (2,517 words) - 20:22, 31 January 2024
  • ...ath>z=2\sin^2(\gamma)</math> (not necessarily this order, but here it does not matter due to symmetry), satisfying that <math>\alpha+\beta=180^{\circ}-\fr ==Solution 2 (pure algebraic trig, easy to follow)==
    15 KB (2,208 words) - 01:25, 1 February 2024
  • == 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 (552 words) - 22:16, 5 June 2024
  • ...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) ==
    11 KB (1,646 words) - 21:14, 28 May 2024
  • (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
  • ...\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
  • ...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
  • ...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 (1,093 words) - 20:38, 10 June 2024
  • ...oint \(C\) on \(\overline{AB}\), distinct from \(A\) and \(B\), that does not belong to any segment from \(\mathcal{F}\) other than \(\overline{AB}\). Th ...</math> passes through <math>C</math> iff <math>a=\frac{1}{2}</math>. It's not hard to convince oneself of this, since the property <math>a^2+b^2=1</math>
    15 KB (2,558 words) - 21:32, 30 May 2024

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)