Coordinates are used to describe the position of points on a grid. The main horizontal line on the grid is known as the x-axis and the main vertical line is the y-axis. Both axes are number lines with ...

Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...

Sketch the graph of the ellipse \(\ds \frac{x^2}{9}+\frac{y^2}{16}=1\) and determine its foci. Let \(C\) be the conic which consists of all points \(P=(x,y)\) such ...

Plot points with coordinates where \(x\) and \(y\) are equal. Three points are sufficient, but more can be plotted. Draw a line through the plotted points. If \(x\) is positive, \(y\) is negative. If ...

A mechanical deformation of a continuum can be expressed as a generalized coordinate transformation of space. Consequently, the equations of electrostatics in deformable media must satisfy covariance ...