Hee fan problem, how to find the area of the fan

A sector has an area of 1c and a circumference of 4cmFind the central angle of the fan and the corresponding chord length.

Solution: Let the radius of the sector be r, the central angle of the circle be , the chord length be b, the arc length be l, the perimeter be p, and the area be s, then there is:

s=(1/2)rl=1...1)

p=2r+l=4...2)

1) (2) The simultaneous solution is r=1cm, l=2cm;

Therefore the central angle of the circle =l r=2 1=2rad=2 180° =.

Chord length b=2rsin( 2)=2 1 sin(

Fan area = 360° *r (angular representation) or Sector area = (1 2)r radian representation).

Arc length = 360° *2 r (angular representation) or arc length = r (radian representation).

Known sector area = 1

i.e. (1 2)r = 1

r²θ = 2 ..

Perimeter d = arc length s + 2r = 4

s + 2r = 4

rθ +2r = 4

4 - 2r) r, substitution *

r² *4 - 2r)/r = 2

r = 1 arc length s = 4 - 2r = 4 - 2(1) = 2 central angle = (4 - 2(1)) (1) = 2, i.e. 2 * 180°

As for the chord length, you have to look at the image.

The central angle of the circle is found, which is equivalent to the length of the third side of the isosceles triangle with the angle of the known triangle.

Set of formulas, the central angle and radius are known, using the cosine theorem.

You need to know the central angle of the fan, and the circle area (360°) is the area of the sector you require.

, is the central angle of the fan, expressed in radians, and r is the radius.

1. Arc length formula.

Angle system calculations.

Radian system calculations.

The absolute value of the radians of the central angle of the circle, r is the radius of the sector.

2. Area formula.

r is the radius of the fan, n is the number of angles of the arc to the center of the circle, is the pi, and l is the arc length corresponding to the fan.

It is also possible to divide the area of the circle in which the sector is located by 360 and multiply it by the angle n of the central angle of the sector as follows:

Derivation process: s= r l 2 r = l r 2

Use the sector area formula or the sector arc length formula.

In junior high school, I said something like this: the formula for the area of the sector, s=n r 2 360. The formula for arc length is, l=n r 180, where n is the number of angles of the central angle of the fan.

After learning the radian system of angles in high school, the formula is simplified as, s=lr 2, and l is the arc length. The arc length l= r, is the radian degree of the central angle of the arc length, which is a real number, and the absolute value should be taken here.

Use this formula to accomplish your task.

It's easy! Divide the arc length by the radius, divide by 2, and multiply by 360°.

For example, if the radius is 1, the arc length is, divide by the radius or, divide by 2 yes, and then multiply by 360° to get 30°.

The arc length is divided by the radius (the sector radius is also OK).

Buy a compass, draw an arc at random, and use an angle to connect the two ends of the arc.

Use a fixed-length rope, a section of fixation, a section of bolt pen, adjust the size of the fan to be drawn, draw a fox, two straight lines to connect the fixed point and the two ends of the arc, you can also use a special drawing ruler, the small one is very cheap. It's also quite practical, and it's useful for our classmates to draw artwork.

Draw a circle. Then go through the center of the circle, draw two diameters, what big the fan shape is, whatever you want.

Knowing the radius r and the circumferential angle a of the sector pair, the arc length is 2 ra 360, plus two radius lengths are the perimeter.

The circumference of the circle is equal to the arc length of the upper sector and is equal to 360 centric angles.