sin(pi/12), using difference of angles formula

TL;DR

This video explains how to find the exact value for the sine of PI/12 (15 degrees) using the angle difference formula.

Transcript

we are going to figure out the exact value for sine of PI over 12 and of course you will be a good idea to work with decrease right so let's go ahead and take PI over 12 which is in radius for now we will just need to multiply by 180 degrees over pi so you see this is now canceled and when we reduce that you end up with 15 and this will be in degre... Read More

Key Insights

• 👨‍💼 The sine of PI/12 (15 degrees) can be found using the angle difference formula.
• 😑 Expressing PI/12 as 15 degrees simplifies the calculations, utilizing known ratios from special angles like 30 and 45 degrees.
• 👨‍💼 The angle difference formula for the sine helps in breaking down the calculation of the sine of 15 degrees into manageable components.
• 🙃 Ratios of sides in special triangles are used to find the values of sine and cosine for 30 and 45 degrees.
• 👨‍💼 Multiplying and subtracting the sine and cosine components of 45 and 30 degrees respectively leads to the exact value of the sine of PI/12 (15 degrees).
• 🫚 The result for the sine of PI/12 is expressed as square root 6 minus square root 2 over 4.
• 🤝 The video emphasizes the importance of dealing with like radicals when adding or subtracting square root terms.

Questions & Answers

Q: What is the angle being discussed in the video?

The video focuses on finding the exact value for the sine of PI/12, which is equivalent to 15 degrees.

Q: How is PI/12 reduced to 15 degrees?

PI/12 is reduced to 15 degrees by multiplying it by 180 degrees/PI, canceling out the radians. This simplifies the angle measurement.

Q: What formulas are used to calculate the sine of 15 degrees?

The video utilizes the angle difference formula for the sine. It expresses the sine of 15 degrees as the sine of 45 degrees times the cosine of 30 degrees, minus the cosine of 45 degrees times the sine of 30 degrees.

Q: How are special angles like 30 and 45 degrees utilized in the calculations?

Special angles like 30 and 45 degrees are used as reference points to simplify the calculations. The ratios of their sides (opposite, adjacent, hypotenuse) are utilized to determine the values for sine and cosine.

Summary & Key Takeaways

• The video demonstrates how to find the exact value for the sine of PI/12 (15 degrees) using the angle difference formula.

• It explains the process of reducing PI/12 to 15 degrees and simplifying it.

• The video also shows how to use the angle difference formula to calculate the sine of 15 degrees.