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Answer: Choice D</h3>
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Work Shown:
L = theta*r
L = (5pi/4)*1
L = 5pi/4
L = 3.92699081698724 approximately
L = 3.927 units
The formula above only works if theta is in radians.
If the angle is in degrees, then you need to convert using the rule
y = (pi/180)*x
where x is the angle in degrees and y is the equivalent angle measure in radians.
In the fourth step, I used my calculator to get that value. You could use pi = 3.14, but in this case, your teacher wants you to use the stored value of pi found in the calculator.
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Extra info (optional section):
If you're curious why that formula works, then consider a circle with circumference C = 2*pi*r. This is the distance around the circle, aka the perimeter.
The arc length in red is only a fractional portion of the full perimeter. Specifically, that fractional amount is theta/2pi. We multiply this fraction by the full perimeter and simplify
L = arc length
L = (full circle circumference)*(fractional amount)
L = (2*pi*r)*(theta/2pi)
L = theta*r
The "2pi" terms cancel in the last step. Again, this formula only works if theta is in radians. This is due to the fractional portion theta/2pi.
There is an equivalent formula for theta being in degrees, which is
L = (theta/360)*2*pi*r
but this version is a bit messier in my opinion.
