Because
radian measure is the ratio of two lengths, it is a unitless measure. For example, in
[link] , suppose the radius were 2 inches and the distance along the arc were also 2 inches. When we calculate the radian measure of the angle, the “inches” cancel, and we have a result without units. Therefore, it is not necessary to write the label “radians” after a radian measure, and if we see an angle that is not labeled with “degrees” or the degree symbol, we can assume that it is a radian measure.
Considering the most basic case, the
unit circle (a circle with radius 1), we know that 1 rotation equals 360 degrees, 360°. We can also track one rotation around a circle by finding the circumference,
$\text{\hspace{0.17em}}C=2\pi r,$ and for the unit circle
$\text{\hspace{0.17em}}C=2\pi .\text{\hspace{0.17em}}$ These two different ways to rotate around a circle give us a way to convert from degrees to radians.
In addition to knowing the measurements in degrees and radians of a quarter revolution, a half revolution, and a full revolution, there are other frequently encountered angles in one revolution of a circle with which we should be familiar. It is common to encounter multiples of 30, 45, 60, and 90 degrees. These values are shown in
[link] . Memorizing these angles will be very useful as we study the properties associated with angles.
Now, we can list the corresponding radian values for the common measures of a circle corresponding to those listed in
[link] , which are shown in
[link] . Be sure you can verify each of these measures.
Finding a radian measure
Find the radian measure of one-third of a full rotation.
For any circle, the arc length along such a rotation would be one-third of the circumference. We know that
Find the radian measure of three-fourths of a full rotation.
$$\frac{3\pi}{2}$$
Converting between radians and degrees
Because degrees and radians both measure angles, we need to be able to convert between them. We can easily do so using a proportion.
$$\frac{\theta}{180}=\frac{{\theta}^{R}}{\pi}$$
This proportion shows that the measure of angle
$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ in degrees divided by 180 equals the measure of angle
$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ in radians divided by
$\text{\hspace{0.17em}}\pi .\hspace{0.17em}$ Or, phrased another way, degrees is to 180 as radians is to
$\text{\hspace{0.17em}}\pi .$
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Got questions? Join the online conversation and get instant answers!