Homogeneous Goniometric Equations
This page introduces homogeneous goniometric equations of the second degree in sine and cosine.
Key points:
• Definition and standard form of homogeneous equations
• Solution methods for different cases a=0,b=0,c=0
• Transformation techniques to simplify equations
Definition: A homogeneous goniometric equation of the second degree has the form a sin²x + b sin x cos x + c cos²x = 0, where a, b, and c are real constants.
Example: For a sin²x + c cos²x = 0, the solution involves finding cos²x = -a / c−a or sin²x = -c / a−c.
The page explains how to recognize and solve various types of homogeneous equations, including those that can be reduced to quadratic form in tan x.