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.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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:  

...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

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.

` `

``

Approved by eNotes Editorial Team