SUMMARY
The discussion focuses on finding the hyperbolic functions sinh(x) and cosh(x) given that tanh(x) = 12/13. Participants confirm that tanh(x) is defined as sinh(x)/cosh(x) and derive coth(x) = 13/12. The correct approach involves using the identity cosh²(x) - sinh²(x) = 1 to establish a system of equations. The solution requires calculating x using the inverse hyperbolic tangent function, tanh⁻¹(12/13), and then substituting back to find sinh(x) and cosh(x).
PREREQUISITES
- Understanding of hyperbolic functions, specifically tanh, sinh, and cosh.
- Familiarity with inverse hyperbolic functions, particularly tanh⁻¹.
- Knowledge of hyperbolic identities, including cosh²(x) - sinh²(x) = 1.
- Basic algebra skills for solving equations involving hyperbolic functions.
NEXT STEPS
- Learn how to derive hyperbolic identities and their applications.
- Study the properties and applications of inverse hyperbolic functions.
- Explore solving systems of equations involving hyperbolic functions.
- Practice problems involving the calculation of hyperbolic functions from given values.
USEFUL FOR
Students studying calculus or advanced mathematics, particularly those focusing on hyperbolic functions and their applications in various mathematical contexts.