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  2. List of trigonometric identities - Wikipedia

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

    Subtracting ⁡ from both sides and dividing by 2 by two yields the power-reduction formula for sine: ⁡ = (⁡ ()). The half-angle formula for sine can be obtained by replacing θ {\displaystyle \theta } with θ / 2 {\displaystyle \theta /2} and taking the square-root of both sides: sin ⁡ ( θ / 2 ) = ± ( 1 − cos ⁡ θ ) / 2 ...

  3. 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.

  4. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    The computation of (1 + ⁠ iπ / N ⁠) N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 + ⁠ iπ / N ⁠) N. It can be seen that as N gets larger (1 + ⁠ iπ / N ⁠) N approaches a limit of −1. Euler's identity asserts that is

  5. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Substituting r(cos θ + i sin θ) for e ix and equating real and imaginary parts in this formula gives ⁠ dr / dx ⁠ = 0 and ⁠ dθ / dx ⁠ = 1. Thus, r is a constant, and θ is x + C for some constant C. The initial values r(0) = 1 and θ(0) = 0 come from e 0i = 1, giving r = 1 and θ = x.

  6. NYT ‘Connections’ Hints and Answers Today, Saturday, December 14

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    2. These words are typically heard when you're placing a bid on something. 3. Related to money and/or monetary units. 4. All of the terms in this category precede a common three-letter noun (hint ...

  7. 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 ...

  8. Las Vegas already seems part of the NBA world, which makes ...

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    Atlanta Hawks' Dyson Daniels (5) defends as Milwaukee Bucks' Giannis Antetokounmpo shoots during a semifinal game in the NBA Cup basketball tournament Saturday, Dec. 14, 2024, in Las Vegas.

  9. Today's Wordle Hint, Answer for #1262 on Monday, December 2, 2024

    www.aol.com/todays-wordle-hint-answer-1262...

    Today's Wordle answer on Monday, December 2, 2024, is GUILE. How'd you do? Next: Catch up on other Wordle answers from this week. Show comments. Advertisement. Advertisement. Holiday Shopping Guides.