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LG 4-4 Arc Length

LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

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Page 1: LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

LG 4-4 Arc Length

Page 2: LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

Arc Length

• An arc of a circle is a segment of the circumference of the circle.

Page 3: LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

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?

3

3

1 3,

2 2

Page 4: LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

• Arc length of a circle in radians

Arc Length = =r

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

Page 5: LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

Find the length of the arc formed by theta:

1. How long is the arc subtended by an angle of radians on a circle of radius 20 cm?

2. How long is the arc subtended by an angle of radians on a circle of radius 5 cm?

7

4

5

3

Find the radian measure for the following:1. In a circle of radius 15 inches an angle intercepts

an arc of 32 inches?

Page 6: LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle

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?