Finding Central Angles from Arc Length and Radius

This video tutorial explains how to find the central angle of a circle given the arc length and radius. The instructor introduces the problem, explains the concept of arc length as a fraction of the circumference, and formulates an equation to solve for the central angle, theta. The video provides step-by-step instructions to solve the equation and offers tips for accurate calculations, including using the fraction button on calculators.

What is the relationship between arc length, central angle, and circumference?

• Arc length is independent of the central angle

• Arc length is a fraction of the circumference based on the central angle

• Arc length equals central angle times radius

• Arc length is directly proportional to the square of the radius

What is the formula for the circumference of a circle?

• C = 2 * r

• C = pi * d

• C = 2 * pi * r

• C = pi * r^2

How do you calculate the central angle when the arc length and radius are known?

• Theta = (L * 360) / (2 * pi * r)

• Theta = (L / C) * 360

• Theta = L / (2 * pi * r)

• Theta = (2 * pi * r) / L

What is the first step to isolate theta in the equation L = (theta/360) * 2 * pi * r?

• Divide both sides by 2 * pi * r

• Subtract L from both sides

• Multiply both sides by 360

• Add 360 to both sides

What is the result of multiplying 360 by 16 in the context of this problem?

• 5760

• 3600

• 5120

• 6144

What is the final step to solve for theta after clearing the denominator?

• Multiply by 14 * pi

• Add 14 * pi to both sides

• Subtract 14 * pi from both sides

• Divide by 14 * pi

What is the correct value of theta when calculated using the formula and given values?

• 140.962 degrees

• 130.962 degrees

• 150.962 degrees

• 120.962 degrees

Why is it important to use the fraction button on a calculator for this calculation?

• To subtract numbers accurately

• To multiply numbers more efficiently

• To ensure the division is handled correctly

• To add numbers without errors

What error might occur if you do not use parentheses when dividing on a calculator?

• The calculator might turn off

• The calculator might perform the operations in the wrong order

• The calculator might add instead of divide

• The calculator might reset its memory

What is the correct way to type the division in a calculator to avoid errors?

• 5760 * 14 / pi

• 5760 + 14 / pi

• 5760 / (14 * pi)

• 5760 / 14 / pi