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

TL;DR

This video explains how to find the exact value of tangent of Pi/12 using the sum or difference formula and special right triangles.

Transcript

okay we're going to figure out the exact value for tangent of Pi / 12 so first of course it would be a good idea to change the pi/ 12 from radians to degrees right so let's go ahead and do that right here pi over 12 and we multiply this by 180° over pi and you see pi and Pi will cancel and when you reduce 180° over 12 you get 15° so this is the sam... Read More

Key Insights

• ✖️ Radians are converted to degrees by multiplying by 180°/Pi.
• 🍹 The sum or difference formula for tangent is used to find the exact value of tangent of a given angle.
• 🔺 Special right triangles can be used to find the values of tangent for certain angles.

Questions & Answers

Q: How do you convert Pi/12 from radians to degrees?

To convert Pi/12 to degrees, you multiply by 180°/Pi. The Pi cancels out, and you get 15°.

Q: How do you use the sum or difference formula for tangent to find the exact value of tangent 15°?

The formula is tangent(a-b) = (tangent(a) - tangent(b)) / (1 + tangent(a) * tangent(b)). Using either 45°-30° or 60°-45°, we can substitute the known values into the formula to find the exact value.

Q: How are special right triangles used to find the values of tangent 45° and tangent 30°?

In a 45-45-90 triangle, tangent is opposite/adjacent, so tangent 45° is equal to 1/1, which simplifies to 1. In a 30-60-90 triangle, tangent is opposite/adjacent, so tangent 30° is equal to 1/sqrt(3).

Q: How do you rationalize the denominator when evaluating the expression for tangent 15°?

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is sqrt(3) - 1. Simplifying the expression gives us the final answer.

Summary & Key Takeaways

• The video teaches how to convert Pi/12 from radians to degrees, which gives the value of 15°.

• The sum or difference formula for tangent is used to find the exact value of tangent 15°.

• Special right triangles, the 45-45-90 triangle and the 30-60-90 triangle, are used to evaluate tangent 45° and tangent 30°.