Find the Exact Value of cos(5pi/12)

TL;DR

Using sum and difference identities for cosine to find the exact value of cosine 5π/12.

Transcript

hello in this video we're going to find the exact value of the cosine of 5 pi over 12. so to do this we're going to use the sum and difference identities for cosine so to do that we have to write this as either a sum or a difference so i'm thinking we can write it as follows so 5 pi over 12 is the same thing as 2 pi over 12 plus 3 pi over 12. and t... Read More

Key Insights

• 🔺 Breaking down angles into smaller components helps in computing trigonometric functions easily.
• 👨‍💼 Memorizing cosine and sine values for common angles simplifies trigonometric calculations.
• 🦻 Understanding cosine sum and difference identities aids in finding precise trigonometric values.

Questions & Answers

Q: How is 5π/12 broken down into π/6 and π/4?

To simplify, 5π/12 is expressed as 2π/12 + 3π/12, which reduces to π/6 and π/4 respectively using common denominators.

Q: What are the cosine values for π/6 and π/4?

The cosine of π/6 is √3/2, and the cosine of π/4 is √2/2.

Q: How are the cosine sum and difference identities applied in this problem?

The cosine sum and difference formula involves multiplying cosine terms, flipping the sign, and multiplying sine terms for the given angles.

Q: What is the final exact value of cosine 5π/12?

The exact value is (√6 - √2) / 4 after evaluating and simplifying the expression.

Summary & Key Takeaways

• Breaks down how to find the exact value of the cosine of 5π/12 using sum and difference trigonometric identities.

• Explains the process of simplifying the angle into smaller components like π/6 and π/4 for easier computation.

• Demonstrates the formula for cosine sum and difference identities involving cosine and sine terms.