What is the vocabulary word for the direction of a curve when points are plotted in the order of increasing values of t?
What is the vocabulary word for the form of the equation of a graph using a pair of parametric equations?
The vocabulary word for the direction of a curve when points are plotted in the order of increasing values of t is "counterclockwise". When you plot points on a curve using parametric equations, you can determine the direction by looking at how the points evolve as the parameter value t increases. If the points move in a counterclockwise manner, then the curve is said to have a counterclockwise orientation.
To determine this direction more formally, you can calculate the derivative of the position vector with respect to t. If the derivative is positive, then the curve is counterclockwise. Conversely, if the derivative is negative, then the curve is said to be in a clockwise direction.
Therefore, to find the vocabulary word for the form of the equation of a graph using a pair of parametric equations, you can consider the term "parametric form" or "parametric representation". When a graph is described using parametric equations, it means that the x and y coordinates are expressed in terms of a parameter, usually denoted by t. This form allows for more flexibility in representing complex curves or shapes that cannot be easily expressed using a single equation in the Cartesian coordinate system.
The vocabulary word for the direction of a curve when points are plotted in the order of increasing values of t is called the "orientation" of the curve.
The vocabulary word for the form of the equation of a graph using a pair of parametric equations is called "parametric form" or "parametric representation."