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If the chord length of the central angle of a circle of 1 radian is equal to 2, then the arc length of the central angle of a circle is equal to () A. sin1 Two B. π Six C. 1 sin1 Two D. 2sin1 Two
Let the radius of the circle be r
2=1，
∴r=1
sin1
2，
The arc length L = α· r = 1
sin1
2．
Therefore, C is selected
In a sector, if the arc length of the central angle is equal to half of the radius, then the number of radians of the central angle is?
[(r/2)/2Лr]*2Л=1/2
If the chord length of the center angle of 1 radian is equal to 2, the arc length corresponding to the central angle of 1 arc is equal to 2. Thank you··
If a = 1 arc of the center angle of the circle, the chord length L = 2, then what is the arc length C of the center angle of the circle equal to?
Let the radius of the circle be r
SIN(A/2)=(L/2)/R
R=(L/2)/(SIN(A/2))
=(2/2)/(SIN(1/2))
=1/(SIN((180/PI)*1/2))
=1/SIN(28.6479)
=2.086
C=A*R
=1*2.086
=2.086
What is the number of radians of the central angle of a chord that is three times the root of the radius? The number of radians of the angle = L / R, so the answer should not be root 3? How can it be 2 / 3 π?
L is the arc length,
Root 3 is the chord length
The chord and radius form the RT triangle
It should be 2 / 3 PI
If the length of an arc is equal to the side length of the inscribed regular triangle of its circle, what is the number of radians of the center angle of the arc?
The radian is D and the radius of circle is r
D = R 3 times the root sign
Circumference length C = 2 π R
Angle = 2 π times (d divided by C) = root three
Given that the arc length of an arc is equal to the side length of the inscribed equilateral triangle of its circle, then the number of radians of the arc to the center angle of the circle is______ .
As shown in the figure,
Δ ABC is an inscribed regular triangle of ⊙ o with radius R,
Then BC = 2CD = 2rsin π
3=
3r，
Let the number of radians of the center angle of the arc be α,
Then R α=
3r，
The solution is α =
3．
So the answer is:
3．
Given that the length of an arc on the circle O is equal to the side length of the inscribed square of the circle, calculate the radians of the central angle of the arc
The diagonal length of the inscribed square is 2R
Then the side length of the square is 2R * (root 2 / 2) = (root 2) r
The arc length is also (radical 2) r
Arc length = center angle * radius
Therefore, the corresponding center angle should be (root 2) radian
If the length of an arc is equal to the side length of the inscribed regular triangle of its circle, then the radian number of its center angle is () A. Three B. 2 Three C. π Three D. 2π Three
Let the radius of the circumscribed circle of the equilateral △ ABC be 2,
Take the midpoint D of BC and connect od and OC, then ∠ OCB = 30 °
According to the deduction of the vertical diameter theorem, OD ⊥ BC,
In RT △ OCD, OD = 1
2OC=1，∴CD=
3, ν side length BC = 2
3．
Let the number of radians of the central angle of the arc to be θ,
Then 2 θ = 2 can be obtained from the arc length formula
3，∴θ=
3．
Therefore, a
Given that the arc length of an arc is equal to the side length of the inscribed equilateral triangle of its circle, then the number of radians of the arc to the center angle of the circle is______ .
As shown in the figure,
Δ ABC is an inscribed regular triangle of ⊙ o with radius R,
Then BC = 2CD = 2rsin π
3=
3r，
Let the number of radians of the center angle of the arc be α,
Then R α=
3r，
The solution is α =
3．
So the answer is:
3．
If the length of the arc is equal to the side length of the inscribed square, what are the radians of the central angle of the circle
Connecting the center of a circle with eight vertices, the vertex angles of the isosceles triangle are all 360 / 8 = 45 degrees
Therefore, the length of the bottom edge is 2rsin (45 / 2) = under the radical sign (2-root 2) (find the formula of sin45 / 2 available half angle )
So the perimeter is:
8 times root sign (2-root2)
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