Mipango

Kikokotoo cha Urefu wa Tao na Eneo la Sekta

Kikokotoo hiki kinatafuta urefu wa tao, eneo la sekta na urefu wa kiambo kutoka nusu kipenyo na pembe ya kati. Pembe zinaweza kuwa kwa digrii au radiani; kwa digrii, majibu yanatolewa kwa usahihi kwa π na pia kwa desimali.

Tokeo

Weka thamani kisha bonyeza Kokotoa ili kuona tokeo.

Fomula

s=θ360∘×2πr=rθ (θ in radians)s = \frac{\theta}{360^\circ} \times 2\pi r = r\theta \ (\theta \text{ in radians})

The arc is the same fraction of the circumference as the angle is of a full turn.

A=θ360∘×πr2=12r2θA = \frac{\theta}{360^\circ} \times \pi r^2 = \tfrac{1}{2} r^2 \theta

The sector is the same fraction of the whole circle’s area.

c=2rsin⁡θ2c = 2r\sin\frac{\theta}{2}

The chord is the straight line joining the ends of the arc.

Jinsi ya kutumia kikokotoo hiki

  1. Enter the radius and the central angle, and choose degrees or radians.
  2. Press Calculate to see the arc length, sector area and chord length.

Mifano iliyotatuliwa

Radius 6, angle 60°

60° is 1/6 of a full turn. Arc = 1/6 × 2π × 6 = 2π ≈ 6.283185.

Sector area = 1/6 × π × 36 = 6π ≈ 18.849556.

Chord = 2 × 6 × sin 30° = 6.

Radius 4, angle 1.5 radians

Arc = rθ = 4 × 1.5 = 6.

Area = ½ × 16 × 1.5 = 12.

Chord = 2 × 4 × sin 0.75 ≈ 5.45311.

A semicircle: radius 10, angle 180°

Arc = half the circumference = 10π.

Area = half the circle = 50π. The chord is the diameter, 20.

Makosa ya kawaida

  • Using s = rθ with θ in degrees; that formula needs radians.
  • Mixing up the diameter and the radius.
  • Confusing the arc (curved) with the chord (straight).

Maswali yanayoulizwa mara kwa mara

How do you find the arc length?

Arc length = (θ/360°) × 2πr for θ in degrees, or s = rθ for θ in radians. For r = 6 and 60°: (60/360) × 12π = 2π.

How do you find the area of a sector?

Area = (θ/360°) × πr², or ½r²θ in radians. A 90° sector of radius 4 has area ¼ × 16π = 4π.

What is the difference between an arc and a chord?

The arc is the curved part of the circle between two points; the chord is the straight line joining them.