What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work.
1 answer:
Let us have a denote the measure of the missing arc length.
Since all circles measures 360°, it is then understood that all circles have an angle of 2π .
arc length = <span>central angle
</span> 2π circumference
substitute values:
<u> a </u> = <span><u> 120° </u>
</span> 2π 360°
multiply them by 2π and cancel out 2π so you will have
a = <u> 24 </u> π<u>
</u> 36
Simplify 24/36 π--2/3π. Thus, the answer to this item is the third option.
(See attached file for clearer work)
<span><u /> <u /></span>
Since all circles measures 360°, it is then understood that all circles have an angle of 2π .
arc length = <span>central angle
</span> 2π circumference
substitute values:
<u> a </u> = <span><u> 120° </u>
</span> 2π 360°
multiply them by 2π and cancel out 2π so you will have
a = <u> 24 </u> π<u>
</u> 36
Simplify 24/36 π--2/3π. Thus, the answer to this item is the third option.
(See attached file for clearer work)
<span><u /> <u /></span>
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