TBIL-Calc Coordinates and Vectors (CO)

Chapter 7 Coordinates and Vectors (CO)

How do we use alternative coordinates and vectors to describe points in the plane?

By the end of this chapter, you should be able to...

Sketch the graph of a two-dimensional parametric/vector equation, and convert such equations into equations of only $x$ and $y .$
Compute derivatives and tangents related to two-dimensional parametric/vector equations.
Compute arclengths related to two-dimensional parametric/vector equations.
Convert points and equations between polar and Cartesian coordinates and equations.
Compute arclengths of curves given in polar coordinates.
Compute areas bounded by curves given in polar coordinates.

Before beginning this chapter, you should be able to...

Write equations of lines using slope-intercept and/or point-slope form (Math is Fun ¹)
Recall special trig values on the unit circle (Khan Academy (1)² and Khan Academy (2)³)
Evaluate functions at variable expressions (Purple Math ⁴)
Find the derivative of a function using methods from Section 2.3, Section 2.4, Section 2.5, and Section 2.6.
Find an integral which computes the arclength of a curve using methods from Section 2.4.