subject: Trigonometry Arc Length [print this page] Introduction to trigonometry arc length:
Arc of a circle is a division of the boundary of the circle. The length of an arc is essentially the length of its element of the circumference. In trigonometry the circumference itself can be measured an arc length. The letter "s" signifies the length of an arc. Let us see the trigonometry arc length.
Trigonometry Arc Length
If we find the arc length first we identified the radian measure.
Radian measure is identified as the ratio of the circumference to the diameter.
In this diagram s can be represent the arc length.
The ratio of either arc length to the radius, s/r, will be the radian determine of the middle angle which to arc subtends.
Radian measure of 'theta=s/r' .
Therefore the length of the arc 's = r theta'
Where,
r - Radius
s - Arc length
?' - Angle'
'Suppose given radius r = 20 and 'central angle is 4.678 radians
Length of the arc 's = r theta'
'Therefore the length of the arc =20 x 4.678'
Therefore the arc length s = 93.56.
Examples for Trigonometry Arc Length
Compute the length of the arc, if the radius is 15 cm, and the central angle is 5.8 radians
Solution:
We recognized the method for radian measure of'theta=s/r' .
Therefore the length of the arc s= r ?
As a result,
s = 15 5.8 = 87 cm
Therefore the arc length s = 87 cm
Example 2 for arc length
Compute the length of the arc, if the radius is 50 cm, and the central angle is 18.565 radians
Solution
We recognized the method for radian measure of'theta=s/r' .
Therefore the length of the arc s= r ?
As a result,
s = 50 18.565 = 87 cm
Therefore the arc length s = 928.25 cm
Example 3 for arc length radius
Calculate the angle of the arc, if the radius is 15 cm, and length of arc is 150 cm
Solution
Given, radius is 15 cm, and length of arc is 150.
We known the formula for radian measure of 'theta=s/r' .
