Arc Length of a Circle Formula - Sector Area, Examples, Radians, In Terms of Pi, Trigonometry

TL;DR

Arc length is calculated by multiplying the angle in radians by the radius, while the area of a sector is found by using one of two formulas based on whether the angle is in radians or degrees.

Transcript

now let's talk about arc length and how to find it so let's say if we have a circle and we only want to find a portion of the arc length of the circle let's say this portion the length of that segment in green is known as s which is the arc length and it's based on the angle theta let's say c is the center of the circle and this is a and b the dist... Read More

Key Insights

• ✖️ Arc length is equal to the angle in radians multiplied by the radius.
• 💱 The formula for finding the area of a sector of a circle changes depending on whether the angle is in radians or degrees.
• 🤨 You can convert an angle from degrees to radians by multiplying it by pi divided by 180.
• 🫠 The formulas for arc length and area of a sector are derived from the basic formulas for circumference and area of a circle.
• ⭕ The fractional part of the circle represented by the angle is used to calculate the area of a sector.
• 😒 It is important to use the correct formula depending on whether the angle is in radians or degrees.
• 🇦🇪 The units for arc length are linear units, while the units for area of a sector are square units.

Questions & Answers

Q: How do you calculate the arc length of a circle?

The arc length can be found by multiplying the angle in radians by the radius. If the angle is in degrees, multiply it by 2 pi divided by 360 and the radius.

Q: What is the formula for finding the area of a sector of a circle?

If the angle is in radians, use the formula one half of theta multiplied by the square of the radius. If the angle is in degrees, use the formula theta divided by 360 multiplied by pi and the square of the radius.

Q: Can you use the same formula to find the arc length and area of a sector?

No, the arc length is calculated using the formula arc length = theta * radius, while the area of a sector is found using different formulas based on whether the angle is in radians or degrees.

Q: How can you convert an angle from degrees to radians?

To convert an angle from degrees to radians, multiply it by pi divided by 180. This will give you the equivalent angle in radians.

Summary & Key Takeaways

• Arc length is the distance along a curve of a circle and can be found by multiplying the angle in radians by the radius.

• The area of a sector of a circle can be calculated using two different formulas: one half of theta multiplied by the square of the radius, or theta divided by 360 multiplied by pi and the square of the radius.

• Arc length can be found by multiplying the angle in radians by the radius, or by multiplying the angle in degrees by 2 pi divided by 360 and the radius.