Evaluating Hyperbolic Trig Functions

TL;DR

Learn how to evaluate hyperbolic trig functions and find the values of hyperbolic sine and cosine for various inputs.

Transcript

in this video we're going to talk about how to evaluate hyperbolic trig functions so what is the value of hyperbolic sine of zero in order to find that answer we need to know the formula for hyperbolic sine of x it's equal to the exponential functions e to the x minus E to the negative x divided by 2. so all we need to do is substitute X 4 0 in tha... Read More

Key Insights

• 🈸 Hyperbolic trig functions involve exponential functions and are useful in various mathematical applications.
• 👻 The formulas for hyperbolic sine and hyperbolic cosine allow us to calculate their values for different inputs.
• 0️⃣ The value of hyperbolic sine of zero is zero, while the value of hyperbolic cosine of zero is one.
• 😑 By using logarithmic properties and simplifying the expressions, we can find the values of hyperbolic trig functions for specific inputs.
• 👨‍💼 Hyperbolic cotangent can be calculated by dividing hyperbolic cosine by hyperbolic sine.
• 🙈 Approximate values can be obtained by considering the magnitude of the exponential terms and ignoring negligible values.
• 🎮 The website mentioned in the video provides access to additional video playlists and exam review videos for further study.

Questions & Answers

Q: What is the formula for hyperbolic sine?

The formula for hyperbolic sine is e^x - e^(-x) / 2. It can be used to evaluate hyperbolic sine for any given input x.

Q: How do you find the value of hyperbolic cosine of zero?

The formula for hyperbolic cosine is e^x + e^(-x) / 2. When evaluating hyperbolic cosine for zero, the value is equal to one.

Q: What is the value of hyperbolic sine for ln2?

To find the value of hyperbolic sine for ln2, substitute ln2 into the formula: e^(ln2) - e^(-ln2) / 2. Simplifying this expression gives the result of 3/4.

Q: How do you calculate the value of hyperbolic cotangent for ln5?

Hyperbolic cotangent can be found by dividing hyperbolic cosine by hyperbolic sine. For ln5, substitute ln5 into the formulas for hyperbolic cosine and hyperbolic sine, simplify, and then divide the two results.

Summary & Key Takeaways

• The hyperbolic sine of zero is equal to zero, while the hyperbolic cosine of zero is equal to one.

• To evaluate hyperbolic trig functions, use the formulas e^x - e^(-x) / 2 for hyperbolic sine and e^x + e^(-x) / 2 for hyperbolic cosine.

• Applying the formulas, the values of hyperbolic sine for ln2 and ln5 are 3/4 and 13/12, respectively.