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  2. Tangent half-angle formula - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle_formula

    Thus each of these angles has a rational value for its half-angle tangent, using tan φ/2 = sin φ / (1 + cos φ). The reverse is also true. If there are two positive angles that sum to 90°, each with a rational half-angle tangent, and the third angle is a right angle then a triangle with these interior angles can be scaled to a Pythagorean ...

  3. List of trigonometric identities - Wikipedia

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

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  4. Proofs of trigonometric identities - Wikipedia

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

    For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six ...

  5. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The formulas for addition and subtraction involving a small angle may be used for interpolating between trigonometric table values: Example: sin(0.755) ⁡ = ⁡ (+) ⁡ + ⁡ () + () where the values for sin(0.75) and cos(0.75) are obtained from trigonometric table. The result is accurate to the four digits given.

  6. Sheriff's deputy who killed Sonya Massey to be released soon ...

    www.aol.com/sheriffs-deputy-killed-sonya-massey...

    Donna Massey mourns the loss of her daughter, Sonya Massey, who was fatally shot in her home by a Sangamon County sheriff's deputy on July 6, 2024.

  7. 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.

  8. Musk's SpaceX preparing to launch tender offer in Dec at $135 ...

    www.aol.com/news/musks-spacex-preparing-launch...

    By Krystal Hu and Kenrick Cai (Reuters) -Elon Musk's SpaceX is preparing to launch a tender offer in December to sell existing shares at a price of $135 per share, two sources familiar with the ...

  9. Sotomayor has no plans to resign from Supreme Court ... - AOL

    www.aol.com/sotomayor-no-plans-resign-supreme...

    Sotomayor, the first Latina on the high court bench, has embraced her role as the chief counterweight to the conservative majority and made clear she has plenty of fight left to give.