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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. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    In astronomy, the angular size or angle subtended by the image of a distant object is often only a few arcseconds (denoted by the symbol ″), so it is well suited to the small angle approximation. [6] The linear size (D) is related to the angular size (X) and the distance from the observer (d) by the simple formula:

  4. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles.

  5. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.

  6. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    All derivatives of circular trigonometric functions can be found from those of sin(x) and cos(x) by means of the quotient rule applied to functions such as tan(x) = sin(x)/cos(x). Knowing these derivatives, the derivatives of the inverse trigonometric functions are found using implicit differentiation.

  7. With all the movement on the first-base market, what's the ...

    www.aol.com/sports/movement-first-market-whats...

    Italian subs from 6 popular sandwich chains, ranked. Food. The Pioneer Woman. This creamy queso dip will score you major points on game day. Lighter Side. Lighter Side. People.

  8. 7 Dow Jones Dividend Stocks that Underperformed the S&P 500 ...

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    The Dow Jones Industrial Average is chock-full of industry-leading blue chip stocks-- many of which pay dividends.But the Dow tends to underperform the S&P 500 during growth-driven rallies when ...

  9. Georgia coach Kirby Smart mistakenly believed Notre Dame's 11 ...

    www.aol.com/kirby-smart-falsely-claims-notre...

    Editor's note: The University of Georgia announced that Kirby Smart's father, Sonny Smart, died early Saturday morning. By almost any measurement, Georgia's Kirby Smart is one of the best coaches ...