7.2 Rotation of Axes

OpenStax Precalculus 2e — Chapter 10, Section 10.4

Learning Objectives

  • Apply the rotation formulas: \(x = X\cos\theta - Y\sin\theta\), \(y = X\sin\theta + Y\cos\theta\)

  • Determine the rotation angle that eliminates the \(xy\) term using \(\cot(2\theta) = \frac{A-C}{B}\)

  • Classify a rotated conic using the discriminant \(B^2 - 4AC\)

  • Sketch conics after rotation to standard position

Key Concepts

To be filled during study.

Practice Problems

To be completed with textbook exercises.

Section Summary

To be written after completing the section.

Study Notes

Personal observations and connections to engineering work.