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  2. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...

  3. 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 ...

  4. List of trigonometric identities - Wikipedia

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

    Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.

  5. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  6. Seniors will pay more for Medicare in 2025. Here's what to know.

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    Medicare's Part B monthly premium is outpacing both inflation and Social Security's cost-of-living adjustment.

  7. Stock market today: Most of Wall Street rises after the Fed ...

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    Most U.S. stocks rose Thursday, as the Federal Reserve cut interest rates again to make things easier for the economy. The S&P 500 climbed 0.7% to add to its surge from the day before following ...

  8. Angelina Jolie Scores Win in Winery Lawsuit Connected to ...

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    Jolie filed for divorce days after a Sept. 14, 2016 flight on a private plane on which Pitt allegedly became abusive while drunk in front of the kids. Pitt, who has since become sober, has denied ...

  9. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Write a 1 in the middle where the three triangles touch; Write the functions without "co" on the three left outer vertices (from top to bottom: sine, tangent, secant) Write the co-functions on the corresponding three right outer vertices (cosine, cotangent, cosecant) Starting at any vertex of the resulting hexagon:

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