## The Essentials of Plane and Spherical Trigonometry |

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A'BC abscissa acute angle angle corresponding check formula circle circular measure co.ordinates colog cologarithm column common logarithm cos2 cosecant cosine cosy cotangents of angles denote distance EXAMPLES expressed find log find the angle find the logarithm find the values following triangles formulae of Art Geometry given elements Given two sides Hence hypotenuse included angle initial line Isin log cos log cot log esc log sin log tan logarithmic sine manner mantissa multiply negative angle Note Number corresponding obtain the formulae ordinate perpendicular to OA polar triangle positive angle prove the formulae radius ratio right angle right triangle ABC rule of Art secant sin B sin sin2 sines and cosines solution Solve the following spherical right triangle spherical triangle Spherical Trigonometry subtract tabular difference tangent terminal line trigonometric functions Whence by Art Whence by definition Whence we obtain

### 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 92 - ACB are measured, and found to be 126° 35' and 31° 48', respectively. Required the distance AB. 1. A flagpole 40 feet in height stands on the top of a tower. From a position near the base of the tower, the angles of elevation of the top and bottom of the pole are 38° 53

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 114 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...