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LG 4-4 Arc Length

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

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**Start at the point (1, 0) and walk around the circle a distance of**

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?

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**Arc length of a circle in radians**

In the Unit Circle, the arc length = theta(in radians). Why?

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**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 5 cm? Find the radian measure for the following: In a circle of radius 15 inches an angle intercepts an arc of 32 inches?

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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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Radian Measure A central angle has a measure of 1 radian if it is subtended by an arc whose length is equal to the radius of the circle. Consider the circle.

Radian Measure A central angle has a measure of 1 radian if it is subtended by an arc whose length is equal to the radius of the circle. Consider the circle.

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