Let’s explore areas in polar coordinates. In the rectangular coordinate system, we use definite integrals to calculate the area under a curve. For instance, if we have a function (y
When describing a curve using polar coordinates, it remains a curve in the (x-y) plane. The relationship between polar and rectangular coordinates is given by (x = r\cos\theta) and (y
A vector-valued function, also known as a vector function, is a mathematical function that maps one or more variables to a set of multidimensional vectors or infinite-dimensional vectors. Let’s explore
Arc Length (Distance Traveled Along a Curve) in Parametric Form If a curve C is given by the parametric equations x = f (t) and y = g (t) such
Let’s explore slopes and tangents for parametric curves. When we work with parameterized curves, we often encounter questions like: How can we calculate the slope of a tangent line to