Consider two circles, centered at the origin, of radii 1 and 2, respectively. In each circle, begin on thepositive x-axis and rotate counterclockwise by an angle of 210.(a) What is the length of the arc associated with this angle in the circle of radius 1? In the circle of radius 2?Also, what are the radian measure of this angle for each circle.
- print Print
- list Cite
Expert Answers
baxthum8
| Certified Educator
calendarEducator since 2013
write464 answers
starTop subjects are Math and Science
An arc length represents a portion of the entire circumference of a circle with 360˚.
The circumference of a circle is defined by the formula: `C = 2pir`
A circle with a radius of 1 has a circumference of:
`C = 2pi*1 = 2pi`
Therefore the arc length would be:
`210/360* 2pi = (7pi)/6` or 3.67 units
A circle with a radius of 2 has a circumference of:
`C=2pi*2 = 4pi`
Therefore the arc length would be:
`210/360* 4pi = (7pi)/3` or 7.33 units
The radian measures are given respectively as:
`(7pi)/6` and `(7pi)/3` as previously found when calculating units.
` `
``
Related Questions
- A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of...
- 1 Educator Answer
- The radius of a circle is 6 inches. If the central angle is 5pi/3, find the length of the...
- 1 Educator Answer
- The length of an arc of a circle (s) is given by the equation: s= r0 Where r is the radius of the...
- 1 Educator Answer
- The circumference of a circle is equal to 72 pi. Find the radius of this circle.
- 1 Educator Answer
- If the radius of a circle is doubled, what effect does this have on the area of the circle? On...
- 1 Educator Answer