How to Find sin(pi/12) Using the Half Angle Formula

TL;DR

To find sin(pi/12), or sin(15 degrees), use the half angle formula: sin(x/2) = √(1 - cos(x))/2. Substitute x with 30 degrees, simplify to get sin(15 degrees) = √(2 - √3) / 2, since the sine value is positive for angles in the first quadrant.

Transcript

I'm going to show you guys how to figure out the except for you for angle PI over 12 then the sine of 15 degrees in this video I will show you guys how to use the half angle Puma for this in one of my previous video I'll show you guys how to use the angle difference formula foil right we wrote sine of 15° as sine of 45 degrees minus 30 degrees insi... Read More

Key Insights

• 💄 The half angle formula is a useful tool in trigonometry, simplifying calculations and making them more manageable.
• 🤘 Positive or negative sign values can be determined based on the location of the angle on the coordinate plane.
• ✖️ Complex fractions within the half angle formula can be simplified through multiplication.

Questions & Answers

Q: What is the purpose of using the half angle formula for trigonometric functions?

The half angle formula allows us to find the sine value of an angle by simplifying it into a smaller and known angle, making calculations easier.

Q: How do we determine whether the sine value will be positive or negative using the half angle formula?

To determine the sign, we refer to the location of the angle on the coordinate plane. If it falls in the first quadrant, the sine value will be positive. If it falls below the x-axis, the sine value will be negative.

Q: How do we simplify a complex fraction within the half angle formula?

To simplify a complex fraction, we eliminate the complex fraction structure by multiplying the top and bottom of the fraction by the denominator of the smaller fraction within the complex fraction.

Q: Can we verify the accuracy of the half angle formula by using a calculator?

Yes, we can input the result obtained using the half angle formula and compare it with the result obtained through a calculator, which should yield the same decimal value.

Summary & Key Takeaways

• The video demonstrates how to apply the half angle formula to find the sine of an angle.

• By using a general formula, the speaker breaks down the steps to determine whether the sine value is positive or negative.

• The video also illustrates how to simplify a complex fraction within the half angle formula.