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Radian system formula about sector arc length and area formula? Derivation formula?
L - arc length
R - radius
S - area
α— fan angle
π - pi
Then: l = π R α/ 180 if α In radians, l = R α
S=πR ²α/ 360 if α In radians, s = R ²α/ two
Calculation formula of sector arc length and area (radian system)
L = Q * r (q is the radian system, representing the center angle of the arc length, and R represents the radius)
The area formula can be recorded by imitating the area formula of a triangle, s = L * r / 2
Given that the chord length of the center angle of 2 radians is 2, then the arc length of the center angle is () A. 2 B. sin2 C. 2 sin1 D. 2sin1
Connecting the center of the circle and the midpoint of the string, a right triangle is formed by the chord center distance, half the chord length and the radius. The half chord length is 1 and the center angle of the opposite circle is also 1
Therefore, the radius is 1
sin1
The arc length opposite the center angle is 2 × one
sin1=2
sin1
So choose C
Given that the chord length of a circle with a center angle of 1 radian is 2, what is it that the arc length of this center angle is sin1 / 2?
Suppose that the chord of the 1rad angle is ab and the center of the circle is O, then the angle AOB is 1rad, ab = 2, radius r = OA = ob, substituting AB = 2 from the sine theorem OA / sin [(π - 1) / 2] = AB / sin1, then OA = 2Sin [(π - 1) / 2] / sin1, OA = 2 [sin (π / 2) cos (1 / 2) - cos (π / 2) sin (1 / 2)] / [2Sin (1 / 2) cos (1 / 2)] = 1
If the chord length of the center angle of 1 radian is 2, the arc length of the center angle is 2
If the chord length of the center angle of a = 1 radian is L = 2, then the arc length of the center angle of a is C?
The arc radius is r
A = 1 radian = 1 * 180 / π = 57.296 degrees
L=2*R*SIN(A/2)
R=(L/2)/SIN(A/2)
=(2/2)/SIN(57.296/2)
=2.0858
C=R*A=2.0858*1=2.0858
It is known that points e, F, G and H are the midpoint of edges AB, BC, CD and Da of quadrilateral ABCD respectively. Verification: vector EF = vector Hg, please draw,
Connect AC
Vector EF = 1 / 2 vector AC
Vector Hg = 1 / 2 vector AC
So vector EF = vector Hg
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