what is the radius of a circle that has a sector area of 3pi cm squared and a central angle of 2pi/3 radians
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None of these. All of these functions are defined as ratio of trigonometric functions.
Trigonometric functions have infinite zeroes, so when you put them in the denominator, they lead to infinitely many points of ill-definition.
Specifically, we have:
which is undefined at
which is undefined at
which is undefined at
which is undefined at