What Is a Radian?

In mathematics and physics, radians are a measure of angle. It is a unit derived from the International System of Units. The unit abbreviation is rad. Definition: An arc with an arc length equal to its radius, and its center angle is 1 radian. (That is, the two rays are emitted from the center of the circle to the circumference, forming an arc with an angle that is exactly opposite the angle. When the length of this arc is exactly equal to the radius of the circle, the arc of the angle between the two rays is 1.)

In mathematics and physics, radians are a measure of angle. It is a unit derived from the International System of Units. The unit abbreviation is rad. Definition: An arc with an arc length equal to its radius, and its center angle is 1 radian. (That is, the two rays are emitted from the center of the circle to the circumference, forming an arc with an angle that is exactly opposite the angle. When the length of this arc is exactly equal to the radius of the circle, the arc of the angle between the two rays is 1.)
Chinese name
radian
Foreign name
radian
Category
Mathematical term
Abbreviation
rad

Radian definition

According to the definition, the number of radians per week is 2r / r = 2, 360 ° angle = 2 radians, so 1 radian is about 57.3 °, which is 57 ° 17'44.806 '', 1 ° is / 180 radians, and the approximate value is 0.01745 In radians, the circumferential angle is 2 radians, the flat angle (that is, 180 ° angle) is radians, and the right angle is / 2 radians.
In specific calculations, when the angle is given in radians, it is usually not written in radians, and the value is directly written. The most typical examples are trigonometric functions such as sin 8, tan (3 / 2).
In junior high school mathematics, we learned the arc length formula:
Arc length = nr / 180, where n is the number of angles, which is the arc length corresponding to the center angle n.
But if we use radians, the above formula will become simpler: (note that radians are positive or negative)
l = | | r, which is the product of the size of and the radius.
Similarly, we can simplify the fan area formula:
S = | | r ^ 2/2 (half the size of the angle and the product of the square of the radius, from which we can see that when | | = 2, which is the peripheral angle, the formula becomes S = r ^ 2, the formula for the area of a circle!)
In the scientific calculation method of the calculator program (Start Programs Accessories Calculator) provided with the Windows operating system, you can call radians for calculation.

Radian special value

degree
0 °
30 °
45 °
60 °
90 °
120 °
135 °
150 °
180 °
270 °
360 °
radian
0
/ 6
/ 4
/ 3
/ 2
2 / 3
3 / 4
5 / 6
3 / 2
2

IN OTHER LANGUAGES

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