**The Quest of**

Arc Signs

Arc Signs

So you're lost in this odd world of numbers and letters...What's it called again? I hear some people call it mathematics.

In the world of mathematics, there are many things to ponder about, but one subject forgotten by many is the subject of arc length.

You right there! I assume that you are bright enough to remember arc length and if it escapes you, wise enough to refresh your memory on this topic. Up for the quest?

On this quest, you will learn how to find the arc length and if you succeed, you get to escape this part of the mathematics world (only for awhile).

To begin, you'll want to know some definitions.

**Start here**

Tangent:

A straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point (meaning intersect it).

Radius:

A straight line from the center to the circumference of a circle or sphere.

Diameter:

a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

Circumference is the distance around a circle.

Chord:

a chord is a line segment joining two points on any curve (a non extended secant).

Secant:

a straight line that cuts through a curve two times.

Tip: Remember this by the saying: "She can't" have just one pair of shoes, she needs two.

Finally...

Arc:

A portion of the circle which is between two radii.

Can you label the parts of a circle?

Answer:

There are a couple more definitions, but we'll go through them along the way. The two for now will be major arc and minor arc.

Major arc: the arc that goes around a larger portion of the circumference.

Minor arc: the arc that goes around a smaller portion of the circumference

Check this website out:

http://www.mathsisfun.com/definitions/major-arc.html

Central Angle:

is an angle vertex is the center of a circle and whose legs (sides) are radii intersecting the circle in two distinct points

There is a relationship between arc length and the central angle.

Arc lenght central angle

=

Circumference 360 degrees

Radian: is an a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius. Arc length of a circle: arc lenght = theta(R) s=theta(R)

Arc lenght of a circle:

arc lenght= theta (x) ( pi/180 x r)

r= radius

The relationship between Degrees and Radian :

Let us try an example:

Convert 200° into radian measure:

Answer:

200 degrees x π/180degrees=10π/9 radians =3.49 radians

But that was only the geometry part of arc signs...

Now for the algebra two part of arc signs.

More Questions:

1. Convert 50 degrees to radians

2. Convert π/6 to degrees

3.How long is the arc subtended by an angle of radians on a circle of radius 20 cm?

Radian Measure of a central angle of a circle :

theta= s/r = length of subtended arc/ radius

subtend=opposite arc

Some Formulas

;

Answers:

1. 50 degrees(π/180)=

50 degrees (5π/ 180)=

5π/18

2. π/6 (180/π)=

(180/6)= 30 degrees

3. S=theta(r) = (7π/4)(20)=

35π= 109.956 cm

Now, look at that! We have come to the end of our quest. If you feel as though you haven't fully mastered the topic, why not take the quest over again? There are also a ton of great videos on Khan Academy.com and questions on Regentsprep.org (from where I got my questions). Thank you for going on this quest with me, may you flourish mathematically.