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Trigonometry

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Difficult

Gear Rotation

TRIG-VE3G4Y

Two connected gears on a machine are rotating as shown below:

The smaller gear has a radius of $4$ centimeters and the larger gear has a radius of $7$ centimeters. Determine the angle (in radians) through which the larger gear has rotated when the smaller gear has made one full rotation.

Round your answer to two decimal places.

A

$2.71$

B

${\pi}$

C

$3.59$

D

$3.6$

E

$3.97$