SUMMARY
The equation sin(80°) * csc(80°) equals 1 due to the definition of the cosecant function, where csc(80°) is the reciprocal of sin(80°). Therefore, sin(80°) * (1/sin(80°)) simplifies directly to 1. Additionally, the expression cos(400°) * sec(40°) also equals 1, as cos(400°) is equivalent to cos(40°), and sec(40°) is defined as 1/cos(40°), leading to the same cancellation effect.
PREREQUISITES
- Understanding of trigonometric functions: sine, cosecant, cosine, and secant.
- Knowledge of angle equivalence in trigonometry, particularly with angles greater than 360°.
- Familiarity with the concept of reciprocals in mathematics.
- Basic algebraic manipulation skills to simplify trigonometric expressions.
NEXT STEPS
- Study the properties of trigonometric functions, focusing on sine and cosecant relationships.
- Learn about angle reduction techniques in trigonometry, especially for angles exceeding 360°.
- Explore the definitions and applications of secant and cosine functions in trigonometric identities.
- Practice simplifying trigonometric expressions using reciprocal identities and angle equivalences.
USEFUL FOR
Students and educators in mathematics, particularly those studying trigonometry, as well as anyone looking to deepen their understanding of trigonometric identities and simplifications.