SUMMARY
The discussion focuses on solving trigonometric problems involving angles x and y in the first quadrant, where sin(x) = 4/5 and cos(y) = 7/25. The exact values for cos(x) and sin(y) are derived using the Pythagorean identity sin²(x) + cos²(x) = 1, leading to cos(x) = 3/5 and sin(y) = 24/25. The compound angle formula sin(x+y) = sin(x)cos(y) + sin(y)cos(x) is utilized to find sin(x+y), resulting in sin(x+y) = (4/5)(7/25) + (24/25)(3/5) = 172/125.
PREREQUISITES
- Understanding of basic trigonometric identities, specifically the Pythagorean identity.
- Familiarity with the sine and cosine functions in the first quadrant.
- Knowledge of compound angle formulas in trigonometry.
- Ability to perform algebraic manipulations with fractions.
NEXT STEPS
- Study the Pythagorean identity and its applications in trigonometry.
- Learn about the unit circle and how it relates to sine and cosine values.
- Explore compound angle formulas in detail, including sin(x+y) and cos(x+y).
- Practice solving trigonometric equations involving multiple angles and identities.
USEFUL FOR
Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to strengthen their understanding of angle relationships in the first quadrant.