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The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

The functions (also called the circular functions) comprising trigonometry: the cosecant cscx, cosine cosx, cotangent cotx, secant secx, sine sinx, and tangent tanx. However, ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.