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  2. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.

  3. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The tangent half-angle substitution relates an angle to the slope of a line. Introducing a new variable = ⁡, sines and cosines can be expressed as rational functions of , and can be expressed as the product of and a rational function of , as follows: ⁡ = +, ⁡ = +, = +.

  4. 2016 North Carolina Tar Heels football team - Wikipedia

    en.wikipedia.org/wiki/2016_North_Carolina_Tar...

    L W L Atlantic Division No. 1 Clemson xy$# 7 – 1 14 – 1 No. 21 Louisville x 7 – 1 9 – 4 No. 8 Florida State 5 – 3 10 – 3 NC State 3 – 5 7 – 6 Wake Forest 3 – 5 7 – 6 Boston College 2 – 6 7 – 6 Syracuse 2 – 6 4 – 8 Coastal Division No. 16 Virginia Tech xy 6 – 2 10 – 4 North Carolina 5 – 3 8 – 5 No. 20 Miami (FL)

  5. Savitch's theorem - Wikipedia

    en.wikipedia.org/wiki/Savitch's_theorem

    def stcon (s, t)-> bool: """Test whether a path of any length exists from s to t""" return k_edge_path (s, t, n) # n is the number of vertices def k_edge_path (s, t, k)-> bool: """Test whether a path of length at most k exists from s to t""" if k == 0: return s == t if k == 1: return (s, t) in edges for u in vertices: if k_edge_path (s, u, floor (k / 2)) and k_edge_path (u, t, ceil (k / 2 ...

  6. Pushforward measure - Wikipedia

    en.wikipedia.org/wiki/Pushforward_measure

    The measure f ∗ (λ) might also be called "arc length measure" or "angle measure", since the f ∗ (λ)-measure of an arc in S 1 is precisely its arc length (or, equivalently, the angle that it subtends at the centre of the circle.) The previous example extends nicely to give a natural "Lebesgue measure" on the n-dimensional torus T n.

  7. Duke QB asks professor for homework extension deadline ... - AOL

    www.aol.com/sports/duke-qb-asks-professor...

    The junior quarterback threw for 175 yards and rushed for 98 yards, including a 44-yard touchdown run as Duke outscored Clemson 22-0 in the second half to record a memorable victory.

  8. List of Louisville Cardinals in the NFL draft - Wikipedia

    en.wikipedia.org/wiki/List_of_Louisville...

    QB 1966: 4 12 60 Doug Buffone: Chicago Bears: LB 6 11 91 Charles Johnson: San Francisco 49ers: DT 17 7 252 Benny Russell: St. Louis Cardinals: QB 1967: 2 13 39 Tom Holzer: San Francisco 49ers: T 13 19 334 Bill Downes: Philadelphia Eagles: DT 15 12 379 Clarence Spencer: San Francisco 49ers: WR 1968: 3 16 71 Ed Harmon: Dallas Cowboys: LB 6 7 145 ...

  9. Minkowski's theorem - Wikipedia

    en.wikipedia.org/wiki/Minkowski's_theorem

    A set in ℝ 2 satisfying the hypotheses of Minkowski's theorem.. In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin).