How to find the degree of the central angle, how to find the degree of the central angle of the circ

Find the central angle. There are three ways to get a degree:

1. The arc length and radius are known.

According to the arc length formula.

l (arc length) = (r 180) x x n (n is the number of angles in the center of the circle, the same below) can be obtained, and the number of angles in the center of the circle is n=180l r.

2. The sector area corresponding to the known central angle.

and radius. According to the formula for calculating the sector area: s (sector area) = (n 360) x r 2, the number of angles in the center of the circle n = 360s r 2.

3. The chord length and radius are known.

According to the formula for calculating the chord length: k (chord length) = 2rsin (n 2), the number of angles at the center of the circle is n = 2arcsin(k 2r).

Scalloped central corners.

n=(180l) (r) unit: (°.)

The degree of the central angle of the circle is equal to the degree of the arc it opposes.

The central angle refers to the AOB formed by the radius at both ends of the arc AB in a circle with the center of O, which is called the central angle of the arc AB. The central angle of the circle is equal to the circumferential angle of the same arc.

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The circumference of the circle = 2 r

The arc is a part of the circle, therefore.

Arc length = circumference of the circle * (number of angles of the center of the circle to which the arc is opposed) 2 r * center angle of 360°

Because 2 = 360°

So the fan-shaped central angle = arc length radius.

The resulting unit is radians, which should be replaced by angles.

Arc length = central angle multiplied by pi multiplied by radius divided by 180 degrees.

Sector area = central angle multiplied by pi multiplied by radius squared divided by 360 degrees.

The degree of the central angle of the circle is equal to the degree of the arc it opposes.

The value range of the central angle is 0°< 360°, that is, (0, 2

Sector Area The area of the circle = the central angle of the circle 360°, so the central angle of the circle = 360° The area of the sector The area of the circle is the inversion of the formula.

The radius of the sector and the length of the arc are known = l r (l is the arc length and r is the radius).

Sector Area The area of the circle = the central angle of the circle 360°, so the central angle of the circle = 360° The area of the sector The area of the circle is the inversion of the formula.

The circumference of the circle = 2 r

The arc is part of the circle, so the arc length = the circumference of the circle * (the number of angles of the center of the circle to which the arc is opposite 360°) = 2 r * the angle of the center of the circle 360°

Because 2 = 360°

So the fan-shaped central angle = arc length radius.

The obtained unit is the number of radians, which should be replaced by the number of angles.

There are three ways to find the degree of the central angle of the circle:

1. The arc length and radius are known.

According to the formula of arc length: l (arc length) = (r 180) x x n (n is the number of angles at the center of the circle, the same below), and the number of angles at the center of the circle is n=180l r.

2. The sector area and radius corresponding to the known central angle.

According to the formula for calculating the sector area: s (sector area) = (n 360) x r 2, the number of angles in the center of the circle n = 360s r 2.

3. The chord length and radius are known.

According to the formula for calculating the chord length: k (chord length) = 2rsin (n 2), the number of angles at the center of the circle is n = 2arcsin(k 2r).

1. The nature of the central angle:

1. The vertex is the center of the circle;

2. Both sides intersect the circumference;

3. Properties of the central angle: in the same circle or equal circle, the arcs of the equal central angles are equal, the chords are equal, and the chord centris of the paired strings is also equal. In the same circle or equal circle, as long as one of the four pairs of quantities is equal, the other three pairs must be equal;

4. The degree of an arc is equal to the degree of the central angle of the circle to which it opposes;

5. The circumferential angle of the semicircle (or diameter) is a right angle; The chord to which the circumferential angle of 90° is aligned is the diameter.

2. Other calculation formulas related to the central angle:

1. The formula for calculating the arc length is l=n r 180, l=r. where n is the number of angles at the center of the circle, r is the radius, and l is the arc length of the center of the circle.

2. S fan = (n 360) r 2 (n is the degree of the central angle of the circle, and r is the radius of the circle corresponding to the fan).

The way to find the degree of the central angle is usually as follows: the length of the arc to which you want the central angle to be divided by the circumference of the circle in which the arc is located and multiplied by 360°. The number you are looking for is the degree of the central angle.

Center angle = 360 times the radius of the base circle divided by the busbar.

I'm much more advanced than you, learn a little!

The number of angles in the center of the circle: the arc length and radius are known, according to the formula of the arc length: l (arc length) = (r 180) x x n (n is the number of angles in the center of the circle, the same below), and the number of angles in the center of the circle is n=180l r.

The sector area and radius corresponding to the central angle of the circle are known according to the formula for calculating the sector area: s (sector area) = (n 360) x r, and the number of the center angle n = 360s r, etc.

180 According to the first sentence, the following equation can be listed: 2pir 2=1 2*l*2pi*r

where r is the radius of the bottom surface and l is the length of the busbar. This can be easily simplified according to the area formula: l=2r

Then, according to the formula of the perimeter of the fan area, there are l*@=2r*@= (the perimeter of the bottom surface) and 2pi*r (the perimeter of the fan obtained from the side, that is, the perimeter of the original bottom surface), so the angle @=pi=180 can be obtained

The degree of the central angle of the circle is equal to the degree of the arc it opposes.

The value range of the central angle is 0°< 360°, that is, (0, 2

The circumference of the circle = 2 r

The arc is a part of the circle, therefore.

Arc length = circumference of the circle * (number of angles of the center of the circle to which the arc is opposed) 2 r * center angle of 360°

Because 2 = 360°

So the fan-shaped central angle = arc length radius.

The resulting unit is radians, which should be replaced by angles.

How do you find the degree of the central angle? As follows:

The number of angles in the center of the circle: the arc length and radius are known, according to the formula of the arc length: l (arc length) = (r 180) x x n (n is the number of angles in the center of the circle, the same below), and the number of angles in the center of the circle is n=180l r.

The sector area and radius corresponding to the central angle of the circle are known according to the formula for calculating the sector area: s (sector area) = (n 360) x r, and the number of the center angle n = 360s r, etc.

How to solve the problem. <>

1. The arc length and radius are known.

According to the arc length formula: Songhu l (arc length) = (r 180) x x n (n is the number of angles in the center of the circle, the same below) can be obtained, and the number of angles in the center of the circle is n=180l r.

2. The sector area and radius corresponding to the known central angle.

According to the formula for calculating the sector area: s (sector area) = (n 360) x r, and the number of circle center angles n = 360s r.

3. The chord length and radius are known.

According to the formula for calculating the chord length: k (chord length) = 2rsin (n 2), the number of angles at the center of the circle is n = 2arcsin(k 2r).

Theorem. The degree of the central angle of the circle is equal to the degree of the arc it opposes.

Relationship with arcs, chords, chord centrax.

In the same circle or equal circle, if one set of quantities is equal in the central distance of two circles, two arcs, two strings, and two chords, the corresponding other groups of quantities are also equal.

Comprehension: (Definition).

1) Equal arc to equal central angle.

2) When dividing the vertex into 360 parts at the circumference of the center of the circle, the angle of the center of each part is 1°.

3) Because the arcs of the central angles of the circle that are equal in the same circle are equal, the whole circle is also divided into 360 parts, and the arc obtained by each part is called the arc of 1° per square mu.

4) The degrees of the central angles of the circle are equal to the degrees of the arcs of their pairs.

Deduction. In the same circle or equal circle, if one of the central distances of (1) two central angles, (2) two arcs, (3) two strings, and (4) two chords are equal, then the rest of the groups of quantities corresponding to them are equal.

The degree formula for the central angle of the circle:

1. l (arc length) = (r 180) n (n is the number of angles of the circle lift, the same below).

2. s(sector area) = n 360) r2.

3. The central angle of the fan-shaped circle is n=(180L) (R) (degree).

4. k=2rsin(n 2) k=chord length; n = the angle of the center of the circle opposite by the string, measured in degrees.

Hello dear! In plane geometry, the central angle refers to the angle corresponding to the arc of the two sides with the center of the circle as the vertice. To find the degree of the central angle of the circle, you can refer to the following method:

Determine the center of the circle: take any point on the Huipai circle, connect the point and the center of the circle, and get a radius; Find the arc: determine the arc corresponding to the central angle, which can be obtained according to the angle given in the question or the length of the arc, or by measurement.

Calculate the number of angles at the center of a circle: According to the definition of a circumferential angle, the circumferential angle of a circle is equal to 360 degrees, so the degrees of the circumferential angle are equal to the degrees of the arc. The arc corresponding to the central angle is a part of the circumferential angle, so the degree of the central angle can be calculated by finding the number of circumferential angles corresponding to the arc.

Specifically, if the number of circumferential angles corresponding to the arc is degrees, then the degrees of the central angle are also degrees. It is important to note that when making calculations, you need to make sure that the angle units used are the same, usually in degrees.