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