page_title: Vector-valued function
section_title: Example: helix
hierarchical_section_title: Vector-valued function / Example: helix
caption_attribution_description: English: This a graph of a parametric curve (a simple vector-valued function with a single parameter of dimension 1). The graph is of the curve: &lt;2Cos(t),4Sin(t),t&gt; where t goes from 0 to 8 pi.
context_page_description: A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector; the dimension of the domain is not defined by the dimension of the range.
context_section_description: A common example of a vector-valued function is one that depends on a single real number parameter t, often representing time, producing a vector v(t) as the result.  In terms of the standard unit vectors i, j, k of Cartesian 3-space, these specific types of vector-valued functions are given by expressions such as
  where f(t), g(t) and h(t) are the coordinate functions of the parameter t, and the domain of this vector-valued function is the intersection of the domain of the functions f, g, and h. It can also be referred to in a different notation:
  The vector r(t) has its tail at the origin and its head at the coordinates evaluated by the function.
  The vector shown in the graph to the right is the evaluation of the function  near t=19.5 (between 6π and 6.5π; i.e., somewhat more than 3 rotations). The helix is the path traced by the tip of the vector as t increases from zero through 8π.
  In 2D, We can analogously speak about vector-valued functions as
   or
caption: A graph of the vector-valued function r(Z) = 〈2 cos Z, 4 sin Z, Z〉 indicating a range of solutions and the vector when evaluated near Z = 19.5
exif: {}