Trigonometric function in Radian-math. h. The parameter is a radian, not an angle.

In mathematics and physics, radians are the measurement units of angles. It is an international unit, abbreviated as rad.

 

Definition 1:The arc with the arc length equal to the radius, and its right center angle is 1 radian. (That is, the two rays are shot from the center of the center to the circumference, forming an arc with a positive angle and an angle. When the arc length is equal to the circle radius, the angle between the two rays is 1 .)

 

According to the definition, the radians of a week are 2 π R/r = 2 π, 360 ° angle = 2 π radians. Therefore, 1 radian is about 57.3 °, that is, 57 ° 17' 44. 806 '', 1 ° is π/180 radian, the approximate value is 0.01745 radian, the circumference is 2 π radians, the horizontal angle (I .e. 180 ° angle) is π radians, And the right angle is π/2 radian.

 

In a specific calculation, when the angle is given in radians, the unit of radians is usually not written and the value is directly written. The most typical examples are trigonometric functions, such as sin 8 π and Tan (3 π/2 ).

 

In junior high school mathematics, we have learned the arc length formula:

 

Arc Length = n2 π R/360. Here N is the angle number, that is, the arc length corresponding to the circle angle n.

 

However, if we use radians, the above formula will become simpler: (Note that radians have positive and negative points)

 

L = | α | r, that is, the product of Alpha size and radius.

 

Similarly, we can simplify the slice area formula:

 

S = | α | r ^ 2/2 (1/2 times the size of the Alpha angle, the product of the square of the radius, from which we can see that when | α | = 2 π, that is, the formula is changed to the formula of S = π R ^ 2, circular area !)

 

In the scientific calculation method of the calculator Program (start in the lower left corner of the Computer → program → attachment → calculator) attached to the Windows operating system, radians can be called for calculation.

 

Table of special angle numbers and radians

 

　　

Degrees	0 °	30 °	45 °	60 °	90 °	120 °	135 °	150 °	180 °	270 °	360 °
Radians	0	π/6	π/4	π/3	π/2	2 π/3	3 π/4	5 π/6	π	3 π/2	2π