## The Essentials of Plane and Spherical Trigonometry |

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A'BC abscissa according acute angle adjacent angle bearing called characteristic circle circular colog computed convenient cos a cos cos x cos² cosine cotangent decimal definition Denoting determined difference distance Dividing equal EXAMPLES expressed figure find the values following triangles formulæ functions Geometry Given greater Hence hour included angle increases length less log csc log sin log tan logarithm manner mantissa measure middle miles multiply negative Note oblique triangles observation obtain opposite perpendicular plane positive produced prove quadrant ratio remaining respectively result right angle rule secant sides signs sin B sin sin x sin² sine solution Solve the following spherical triangle subtract supplement taken tanc tangent triangle ABC Trigonometry values Whence

### Popular passages

Page 105 - If the function is a sine, since the sine of an angle is equal to the sine of its supplement...

Page 102 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 75 - 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 74 - 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 94 - 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 55 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 54 - The logarithm of a product is equal to the sum of the logarithms of its factors.

Page 48 - In the formula sin (x + y) = sin x cos y + cos x sin y...

Page 113 - 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 94 - 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...