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  2. Proofs of trigonometric identities - Wikipedia

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

    This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin ...

  3. List of trigonometric identities - Wikipedia

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

    The fact that the triple-angle formula for sine and cosine only involves powers of a single function allows one to relate the geometric problem of a compass and straightedge construction of angle trisection to the algebraic problem of solving a cubic equation, which allows one to prove that trisection is in general impossible using the given tools.

  4. Law of tangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_tangents

    In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective

  5. Pythagorean trigonometric identity - Wikipedia

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

    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 involving the cotangent and the cosecant also follows from the Pythagorean theorem.

  6. Today's Wordle Hint, Answer for #1274 on Saturday, December ...

    www.aol.com/todays-wordle-hint-answer-1274...

    Today's Wordle Answer for #1274 on Saturday, December 14, 2024. Today's Wordle answer on Saturday, December 14, 2024, is DROOL. How'd you do? Next: Catch up on other Wordle answers from this week.

  7. Trump tariffs on Canada imports could bring sharply higher ...

    www.aol.com/trump-tariffs-canada-imports-could...

    "For a lot of the U.S., it could be problematic for what they pay at the pump," De Haan said of the tariffs' impact, in particular to inland regions such as the Great Lakes, Midwest and the Rockies.

  8. FACT CHECK: Can Donald Trump Actually Run For A Third ... - AOL

    www.aol.com/fact-check-donald-trump-actually...

    A post on X shows Trump ally Steve Bannon stating that President-Elect Donald Trump can actually run for a third term as President by law. Verdict: False The 22nd amendment of the U.S ...

  9. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A. As is shown, H and A are almost the same length, meaning cos θ is close to 1 and ⁠ θ 2 / 2 ⁠ helps trim the red away. ⁡