A small question about the mathematical radian system. Solve a problem in radian math

Don't be discouraged. Take your time to understand. For simplicity, you can set the radius of the circle to the radian of the radius length of r.

Where, radian: understood as a segment of a circle.

The previous sentence can be understood as: The length of a segment of a circle is r.

Then the central angle corresponding to this arc is called the angle of 1 radian, and in this concept, you first understand the concept of arc and central angle, and then it is simple to understand.

In order to make it easier to remember, it is best to draw the diagram and find the arc and the central angle yourself.

Encounter the unit chief. You can interpret the unit length as the number 1

A unit circle (i.e., a circle with a radius of 1).

This sentence: The absolute value of the radian of the angle is equal to the arc length of the central angle is understood in reverse:

The length of the arc to which the central angle is paired is equal to the absolute value of the radians of the angle.

In this way, it is a matter of calculating the arc length of the central angle in radians.

Radian|*Radius r = arc length.

Because radius r=1

So |Radian|*Radius r = arc length.

Here the radian is absolute because the angle is positive and negative.

It is recommended that you take a look at the links below.

Hope it helps.

1.If the length of the arc is equal to the length of the radius, the central angle corresponding to the arc is said to be "the angle of 1 radian".

is another expression of angle and the size is:

1 (degree) = 180 (radian), 1 (radian) = 180 degrees 2The arc length of the central angle = r 180, r = 1, i.e. the arc length = 180

Since 1 (degree) = 180 (radians), the absolute value of the number of radians of the angle = times 180 (radians) = 180 is equal to the arc length.

3.Conversion formula: angle 180 = radan x

The first is the definition of radians, which requires that in the same circle, when the length of an arc is equal to the length of the radius, the size of the angle formed by connecting the two ends of the arc with the center of the circle is 1 radian.

The second is a special case of the arc length formula, which is l=|The number of radians of the angle|*r is r=1 in the unit circle, so it becomes the radians of l== angles|

This topic does not stipulate that the radian system must be used, and the cosine theorem can be used to calculate that the angle b is 150° or 5 6, and it will not be wrong. It will not be judged wrong in the college entrance examination. Because the answer to the college entrance examination can stand up to scrutiny!

First of all, if this question is written in degrees, it should be 150°. Theoretically, it will not be wrongly judged when it is written as a degree, and even if it is wrong, it can be corrected by arguing for reason.

Then in terms of whether you have to use the radian system, it is not necessarily theoretical, but I personally recommend using the radian system.

1) After learning the radian, the questions are all based on the radian system, and it is easy to be confused when taking the angle to do the questions. In addition, the calculation of the radian system is more convenient. For example, when comparing the length of an arc and a straight line, the arc length calculated by the radian can be directly compared with the length of the straight line.

2) Although it is written as degrees, it is theoretically fine, as long as the answer is correct, points should be given. However, in the college entrance examination, if you only use the degree, there may be misjudgment, and the score of the college entrance examination will only care whether the score is omitted, and will not care whether there is a misjudgment. Therefore, it is very likely that you will suffer a loss in the college entrance examination.

Let the diameter d, the corresponding center of the arc excite the sail angle, and the pi hail, then the arc arc length formula is grinding as:

l=πdα÷360

Sector circumference = arc length + 2r

You have to understand the most important =180 degrees=

For example, if you know a degree, you multiply it by 180 degrees

To know a radian, multiply it by (180 degrees).

The content of the red box, ** is the definition of radians.

Definition: The central angle equal to the length of the radius is called the 1 radian angle.

The circumference of a circle with radius r is 2 r, and the central angle of the entire circumferential pair is 360°, also known as the circumferential angle. According to the definition of radian, the radian of the perimeter angle is 2 r r=2 ; The degree of 1 radian is 360° 2 = 180° About: The angle of 2 radian is the degree of = 2·180° 360°

Not to mention that in future calculus calculations, radians are commonly used to derive certain formulas.

The radian system is also used to describe the number of such quantities as the circumferential frequency of some waves.

The unit rad can be omitted and not written.

As for why there are and integers.

In a circle, the angle of the central angle of the circle is certain, then this angle corresponds.

The length of the arc. It has something to do with the radius of the circle, the larger the radius, the longer the arc.

In the same way, if two sectors with the same angle at the center of the circle, the radius will be larger if the arc is long.

The result is:

The central angle of the circle is the same, then.

Arc length 1 divided by radius 1 = arc length 2 divided by radius 2 = a fixed value, which is related to the central angle of the circle.

However, it is too cumbersome to do mathematical calculations directly with angles, so it is defined.

The arc length is the same as the radius length of the circle.

The central angle of the arc is 1 radian, which is 1rad

This is where the whole number appears.

The radian of a whole circle = the arc length of the whole circle divided by the radius = 2, because the circumference is 2 r and the radius is r

To put it bluntly, it is to express the ratio of its corresponding arc length to radius in an angle.

For example, a 60° angle with a radius of 1 arc length is.

r, the radian is 3

RAD I say this for ease of understanding, and the actual development is not estimated to be like this.