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Understanding Arc Length in Circles: Radians and Curves Explained

This article explores the concept of arc length in circles by focusing on the relationship between angles in radians and the distances traveled along the circumference. It begins by defining an arc as a segment of the circle's circumference, discussing how to calculate the length of an arc based on its central angle. The piece includes practical examples, such as finding arc lengths for circles of varying radii and offers a bonus problem involving the movement of a clock's minute hand. Perfect for students learning geometry!

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Understanding Arc Length in Circles: Radians and Curves Explained

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Presentation Transcript

  1. LG 4-4 Arc Length

  2. Arc Length • An arc of a circle is a segment of the circumference of the circle.

  3. Start at the point (1, 0) and walk around the circle a distance of radians. We will arrive at a point . The distance traveled, t, is shown in red.  At the right of the circle is a red line segment that ends in a blue point that is exactly the same length as the red arc ending in the blue point. What is the distance that we walked?

  4. Arc length of a circle in radians In the Unit Circle, the arc length = theta(in radians). Why?

  5. Find the length of the arc formed by theta: • How long is the arc subtended by an angle of radians on a circle of radius 20 cm? • How long is the arc subtended by an angle of radians on a circle of radius 5cm? Find the radian measure for the following: • In a circle of radius 15 inches an angle intercepts an arc of 32 inches?

  6. Bonus Given a clock with minute hand 6 cm long how far does the tip of the hand move from 12:05 to 12:20?

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