Question

explore radian measure by following these steps.

1. move point k to set ( mangle jpk ) to 1 radian. for both circles, what is the relationship between the arc length and radius? arc length = radius
2. move point k to set ( mangle jpk ) to 2 radians. for both circles, what is the relationship between the arc length and radius?

options:
arc length = radius
arc length = ( 2 \times ) radius
arc length = radius ( - 2 )
( mangle jpk = 2.00 ) radians
inner circle
( pg = 1.00 ) units
length of ( gh = 2.00 ) units
outer circle
length of ( jk = 6.00 ) units
( pj = 3.00 ) units

Explanation:

Step1: Analyze Inner Circle

Inner circle radius \( PG = 1.00 \) units, arc length \( GH = 2.00 \) units. Check \( 2\times PG = 2\times1 = 2 \), which equals \( GH \).

Step2: Analyze Outer Circle

Outer circle radius \( PJ = 3.00 \) units, arc length \( JK = 6.00 \) units. Check \( 2\times PJ = 2\times3 = 6 \), which equals \( JK \).

Step3: Determine Relationship

For both circles, arc length is \( 2 \times \) radius.

Answer:

arc length = 2 × radius