There is a road construction brigade to build an arc-shaped curve, whose radius R is 36cm, and the center angle of the arc is 60 degrees, then how many cm is the length of the curve, expressed in π

The length of this curve is 2 × r × π × 60÷360=2 × thirty-six × π × 60÷360=12π cm

Given that the length of an arc is equal to the circumference of the inscribed square of its circle, the absolute value of the radian number of its center angle is urgent!

Square perimeter: 4 √ 2 * r
And arc length: 4 √ 2 * r
Just change the radians with the formula (I forgot)

If the length of an arc is exactly equal to the side length of the inscribed regular triangle of its circle, find the radians of the center angle of the circle? Its answer is root three. I always think it's wrong. By the way, write the process Share to: 2010-07-13 19:33 adopted by the questioner Length of arc = root 3 Radians of circle center angle Radians = (1 / 2) * L / R The radian number of one cycle is 2 π R / r = 2 π, 360 ° angle = 2 π radian I can't understand the process, that is, the radians = (1 / 2) * L / R And how to get the answer to root 3

The man's answer is indeed wrong
Radian equal to its inscribed regular triangle means that it is one third of the circumference, that is, 2 π / 3

Given that the length of the arc is equal to the side length of the inscribed regular triangle in the circle, try to find the radian number of the center angle of the arc

The chord length represented by the edge of an equilateral triangle in a circle is 2 π / 3 to the center angle of the circle
‡ side length of regular triangle = 2 * {rsin [(2 π / 3) / 2]} = 2 * {rsin (π / 3)} = R radical 3
Length of arc L = R root 3
According to L = R θ
θ= L / r = R root 3 / r = root 3 (radian)

Formula for conversion of center angle radian The relation of L s a is the one of the formula. I just didn't read math books.

Center angle = degrees of arc
You may ask: what is the degree of the arc?
Radian = arc length * 2 π / circumference, this is radian, not angle!
π (radian) = 180 °, of course, 2 π = 360 °
1 radian ≈ 57.3 ° in a circle, the center angle can be expressed in radians, for example, the center angle = 1.3 π
Where: π is the PI

Conversion formula of radian and angle

Angle to radian π / 180 × angle
Radian variable angle 180 / π × radian

There is a road construction brigade to build an arc-shaped curve, whose radius R is 36cm, and the center angle of the arc is 60 degrees, then how many cm is the length of the curve, expressed in π