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  2. Pythagorean trigonometric identity - Wikipedia

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

    In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...

  3. Proofs of trigonometric identities - Wikipedia

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

    The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ.

  4. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    The half-angle formula for cosine can be obtained by replacing with / and taking the square-root of both sides: ⁡ (/) = (+ ⁡) /. Sine power-reduction formula: an illustrative diagram. The shaded blue and green triangles, and the red-outlined triangle E B D {\displaystyle EBD} are all right-angled and similar, and all contain the angle θ ...

  5. Pitot theorem - Wikipedia

    en.wikipedia.org/wiki/Pitot_theorem

    A tangential quadrilateral is usually defined as a convex quadrilateral for which all four sides are tangent to the same inscribed circle. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2]

  6. Tangential quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Tangential_quadrilateral

    If the incircle is tangent to the sides AB, BC, CD, DA at T 1, T 2, T 3, T 4 respectively, and if N 1, N 2, N 3, N 4 are the isotomic conjugates of these points with respect to the corresponding sides (that is, AT 1 = BN 1 and so on), then the Nagel point of the tangential quadrilateral is defined as the intersection of the lines N 1 N 3 and N ...

  7. '1923' actress died for 3 minutes, suffered complete organ ...

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    The next day, she said she woke up feeling "very weak" like she couldn't walk. She'd had plans to travel to Las Vegas to film a commercial, and a family member drove her there from her home in L.A ...

  8. Trump announces new ambassadors to Portugal, Malta - AOL

    www.aol.com/trump-announces-ambassadors-portugal...

    President-elect Trump announced two new foreign ambassadors on Tuesday in a Truth Social post. “It is my great honor to announce that John Arrigo will serve as the next United States Ambassador ...

  9. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    A similar proof uses four copies of a right triangle with sides a, b and c, arranged inside a square with side c as in the top half of the diagram. [6] The triangles are similar with area 1 2 a b {\displaystyle {\tfrac {1}{2}}ab} , while the small square has side b − a and area ( b − a ) 2 .

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