In a process with continuous paper, the paper passes across three rollers of radii 3 inches, 4 inches, and 6 inches.


The centers of the three inch and six inch rollers are d inches apart, and the length of the arc in contact with the paper on the four inch roller is s inches.

a. use the law of cosines to write an equation giving the relationship betweeen d and theta

b. Write theta as a function of d

c. Complete the table (view the table in this link
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1 Answer

a) d²=(3+4)²+(4+6)²-2(3+4)(4+6)cosθ=49+100-140cosθ=149-140cosθ.

b) θ=arccos((149-d²)/140)

c) arc/circumference=angle/360; s/8π=(360-θ)/360 so s=(360-θ)π/45.

d (inches) θ (degrees) s (inches)
9 60.94 20.88
10 69.51 20.28
12 87.95 18.99
13 98.21 18.28
14 109.62 17.48
15 122.88 16.55
16 139.84 15.37


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