Johann Lambert expressed this function as the continued fraction "x over one minus x-squared over three minus x-squared," and so on. The hyperbolic type of this function is equal to "e to the two x minus one over e to the two x plus one." The parametric equations "x equals secant of t" and "y equals this function of t" describe an east-west opening hyperbola with semi-major and semi-minor axes of one. The Maclaurin series for this function begins "x plus x-cubed over three plus two x to the fifth over fifteen," and this function's derivative is secant-squared. For 10 points, name this function defined as sine over cosine, or the ratio of opposite to adjacent sides in a right triangle.
Johann Lambert expressed this function as the continued fraction "x over one minus x-squared over three minus x-squared," and so on. The hyperbolic type of this function is equal to "e to the two x minus one over e to the two x plus one." The parametric equations "x equals secant of t" and "y equals this function of t" describe an east-west opening hyperbola with semi-major and semi-minor axes of one. The Maclaurin series for this function begins "x plus x-cubed over three plus two x to the fifth over fifteen," and this function's derivative is secant-squared. For 10 points, name this function defined as sine over cosine, or the ratio of opposite to adjacent sides in a right triangle.
Johann Lambert expressed this function as the continued fraction "x over one minus x-squared over three minus x-squared," and so on.
tangent [accept addition of "of x" or any other variable]