SUMMARY
The discussion centers on solving the trigonometric identity equation cos(2x) = cos(x). The correct solutions for x are 0° and 120°, as confirmed by substituting values back into the equation. The identity used to simplify the equation is cos(2x) = cos²(x) - sin²(x). Misinterpretations of the solutions, such as equating 180° with 0°, were clarified, emphasizing the importance of accurate substitution in verifying solutions.
PREREQUISITES
- Understanding of trigonometric identities, specifically cos(2x).
- Familiarity with the unit circle and angle measures in degrees.
- Basic algebraic manipulation skills for solving equations.
- Knowledge of sine and cosine functions and their properties.
NEXT STEPS
- Study the derivation and applications of the double angle formulas in trigonometry.
- Learn how to solve trigonometric equations using substitution methods.
- Explore the unit circle to better understand angle relationships and values.
- Practice solving various trigonometric identities and equations for different angles.
USEFUL FOR
This discussion is beneficial for students studying trigonometry, educators teaching trigonometric identities, and anyone looking to improve their problem-solving skills in trigonometric equations.
