Download Section 32 r r How many radians in one full circle? How many

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Transcript 
Section 3­2
Often when we talk about angles we use a different kind of measure than degrees.
1 radian = the central angle of an arc which is the length of the radius
r
How many radians in one full circle?
θ r
How many radians in a half circle?
How many radians in 3/4 of a circle?
How do you find the central angle if you have the radius and the arc length?
θ=
arc length
radius
S
or θ = r
which also means that S = rθ
That is, the arc length = radius times the angle in radians.
Section 3.2 #8
LA and New York City are approximately 2500 miles apart on the surface of the earth. Assuming that the radius of the earth is 4000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has LA on one side and NYC on the other.
LA
2500 mi
NYC
θ
i
m
00
40
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