Find the Hyperbolic Functions of u Given that csch(u) = 5/12

TL;DR

Given a hyperbolic cosecant of u as 5/12, find hyperbolic sine, cosine, secant, tangent, and cotangent of u.

Transcript

hi everyone in this problem we're told that the hyperbolic uh cosecant of u is equal to 5 over 12 and we have to find the other five um hyperbolic uh functions let's go ahead and work through it so we'll start by finding the reciprocal of this so a hyperbolic sine of u is just the reciprocal of a hyperbolic cosecant so you just flip it so you get 1... Read More

Key Insights

• ❓ Reciprocal relationships simplify finding hyperbolic functions.
• 🦻 The popular identity aids in finding hyperbolic cosine.
• 👨‍💼 Hyperbolic tangent and cotangent are derived using hyperbolic sine and cosine.
• ➕ Plus/minus sign is crucial in determining the hyperbolic cosine of u.

Questions & Answers

Q: How do you find the hyperbolic sine of u in relation to the given hyperbolic cosecant of u?

To find the hyperbolic sine of u, simply take the reciprocal of the given hyperbolic cosecant of u, resulting in 12/5.

Q: What is the relationship between hyperbolic cosine and hyperbolic sine in hyperbolic functions?

Hyperbolic cosine and hyperbolic sine are reciprocals of each other, making it easy to find one when the other is known.

Q: How do you calculate the hyperbolic tangent of u using hyperbolic sine and cosine?

By dividing the hyperbolic sine of u by the hyperbolic cosine of u, you can determine the hyperbolic tangent of u as 12/13.

Q: Why is the hyperbolic cosine of u expressed as plus/minus 13/5?

The plus/minus sign is used because hyperbolic cosine can only be positive, and the average of e to the u and e to the negative u is always positive.

Summary & Key Takeaways

• Given hyperbolic cosecant of u as 5/12, find hyperbolic sine of u as 12/5.

• Use reciprocal relationships to find hyperbolic cosine, secant, tangent, and cotangent of u.

• Utilize the popular identity to find the hyperbolic cosine of u as plus/minus 13/5.