SUMMARY
The discussion focuses on solving for cos(x/2) and sin(x/2) given that cos(x) = -7/9 in the third quadrant. The correct approach involves using the half-angle identities, specifically sin²(x/2) = (1 - cos(x))/2. Participants confirm that this method is valid and provide guidance on simplifying the results. The final expressions for sin(x/2) and cos(x/2) are derived from these identities, ensuring the correct signs are applied based on the quadrant.
PREREQUISITES
- Understanding of trigonometric identities, specifically half-angle formulas.
- Knowledge of the unit circle and the properties of angles in different quadrants.
- Ability to simplify square roots and fractions.
- Familiarity with the cosine function and its values in various quadrants.
NEXT STEPS
- Study the derivation and application of half-angle identities in trigonometry.
- Practice solving trigonometric equations in different quadrants.
- Explore the unit circle to reinforce understanding of angle signs and values.
- Learn how to simplify square roots and rational expressions effectively.
USEFUL FOR
Students studying trigonometry, educators teaching trigonometric identities, and anyone needing to solve trigonometric equations involving half-angle formulas.
Also, there's one little thing you're forgetting. MrAnchovy mentions it in his post.