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  2. List of trigonometric identities - Wikipedia

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

    The line segment ¯ has length ⁡ and sum of the lengths of ¯ and ¯ equals the length of ¯, which is 1. Therefore, cos ⁡ 2 θ + 2 sin 2 ⁡ θ = 1 {\displaystyle \cos 2\theta +2\sin ^{2}\theta =1} .

  3. Pythagorean trigonometric identity - Wikipedia

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

    A calculation confirms that z(0) = 1, and z is a constant so z = 1 for all x, so the Pythagorean identity is established. A similar proof can be completed using power series as above to establish that the sine has as its derivative the cosine, and the cosine has as its derivative the negative sine.

  4. Proofs of trigonometric identities - Wikipedia

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

    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 θ < θ. So we have ⁡ < <. For negative values of θ we have, by the symmetry of the sine function

  5. De Moivre's formula - Wikipedia

    en.wikipedia.org/wiki/De_Moivre's_formula

    The expression cos x + i sin x is sometimes abbreviated to cis x. The formula is important because it connects complex numbers and trigonometry. By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos nx and sin nx in terms of cos x ...

  6. cis (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Cis_(mathematics)

    cis is a mathematical notation defined by cis x = cos x + i sin x, [nb 1] where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle between line to point and x-axis in polar form).

  7. The Holiday cottage doesn’t actually exist – but here are 10 ...

    www.aol.com/10-cosy-cotswolds-cottages-live...

    1. Laundry Cottage, Bath. We had to do a double take when we first saw Laundry Cottage – it looks uncannily like the little gem from The Holiday. This beautiful Grade II-listed stone house is ...

  8. Passengers duct tape man who allegedly tried to open door ...

    www.aol.com/passengers-duct-tape-man-allegedly...

    A group of passengers sprung into action and stopped a man who allegedly tried to open the cabin door mid-flight during a trip to Dallas Tuesday morning by restraining him with duct tape ...

  9. ‘Busiest Thanksgiving ever’ for air travel with more than 18M ...

    www.aol.com/busiest-thanksgiving-ever-air-travel...

    This Thanksgiving is expected to be the busiest ever for air travel, with a record-setting 18 million Americans expected to jet off for their holiday celebrations in the coming days.