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  2. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    Sine and cosecant begin their period at (where is an integer), finish it at +, and then reverse themselves over + to +. Cosine and secant begin their period at 2 π k , {\displaystyle 2\pi k,} finish it at 2 π k + π . {\displaystyle 2\pi k+\pi .} and then reverse themselves over 2 π k + π {\displaystyle 2\pi k+\pi } to 2 π k + 2 π ...

  3. List of trigonometric identities - Wikipedia

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

    The trigonometric functions are periodic with common period , so for values of θ outside the interval (,], they take repeating values (see § Shifts and periodicity above). Angle sum and difference identities

  4. Periodic function - Wikipedia

    en.wikipedia.org/wiki/Periodic_function

    A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive [2] constant P with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period.

  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. Gudermannian function - Wikipedia

    en.wikipedia.org/wiki/Gudermannian_function

    Graph of the inverse Gudermannian function. ... to be the integral of the hyperbolic secant [3] ... is a periodic function of period ...

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  8. 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 ...

  9. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    According to the New York Times, here's exactly how to play Strands: Find theme words to fill the board. Theme words stay highlighted in blue when found.