## The Essentials of Plane and Spherical Trigonometry |

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A'BC abscissa acute angle AD² adjacent aid of Art angle corresponding BD OD BD CD² check formula circular measure colog cologarithm cos a cos cos(x cos² cosecant cosine cot² cotangent denote distance equal EXAMPLES expressed find log find the angle find the logarithm find the values following triangles formulæ of Art Geometry given elements Given log Given the three Given two sides Hence hypotenuse included angle initial line log cot log csc log sin log tan loga logarithmic sine manner mantissa negative angle Note Number corresponding obtain the formulæ opposite angles ordinate perpendicular plane positive radius ratio result right angle secant sin B sin sin² sine siny solution Solve the following spherical right triangle spherical triangle Spherical Trigonometry subtract tanc tangent terminal line trigonometric functions Whence by Art Whence we obtain XOP₁ ов

### Popular passages

Page 107 - If the function is a sine, since the sine of an angle is equal to the sine of its supplement...

Page 104 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 77 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.

Page 76 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Page 96 - If two sides of a spherical triangle are unequal, the angles opposite them are unequal, and the greater angle lies opposite the greater side ; and conversely.

Page 57 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 56 - The logarithm of a product is equal to the sum of the logarithms of its factors.

Page 50 - In the formula sin (x + y) = sin x cos y + cos x sin y...

Page 115 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...

Page 96 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...