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11 results for “circle”

Formulae (11)

A = \pi r^2

The area enclosed by a circle.

C = 2\pi r

The perimeter (boundary length) of a circle.

s = r\theta

Length of a circular arc (θ in radians).

A = \frac{1}{2} r^2 \theta

Area of a circular sector (θ in radians).

R = \frac{abc}{4K}

Radius of a triangle circumscribed circle.

r = \frac{K}{s}

Radius of a triangle inscribed circle.

s = r\theta

Arc length from radius and central angle in radians.

A = \frac{1}{2}r^2\theta

Area of a circular sector with angle in radians.

\sin^2\theta + \cos^2\theta = 1

The fundamental trig identity from the unit circle.

d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Shortest distance between two points on the Earth for long-range navigation.

d = 2r\arcsin\sqrt{\sin^2\frac{\Delta\phi}{2} + \cos\phi_1\cos\phi_2\sin^2\frac{\Delta\lambda}{2}}

Great-circle distance between two lat/long points.