## The Essentials of Plane and Spherical Trigonometry |

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### Common terms and phrases

A'BC abscissa acute angle adjacent angle angle corresponding characteristic check formula circle circular measure co.ordinates colog cologarithm column common logarithm cos2 cosc cosecant cosine cosy cotangents of angles denote distance Dividing 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 cot log esc logarithmic sine manner mantissa multiply negative angle Note Number corresponding obtain the formulae ordinate perpendicular to OA polar triangle positive angle prove the formulae quadrant radius ratio right angle right triangle ABC rule of Art secant second quadrant sin2 sines and cosines sinJ solution Solve the following spherical right triangle spherical triangle SPHERICAL TRIGONOMETRY subtract tabular difference tangent terminal line trigono trigonometric functions Whence by Art Whence by definition Whence we obtain

### Popular passages

Page 1 - To express fractional parts of the unit, the degree is divided into sixty equal parts called minutes, and the minute into sixty equal parts, called seconds. Degrees, minutes, and seconds are represented by the symbols, °. ', ", respectively. Thus, 43° 22' 37" represents an angle of 43 degrees, 22 minutes, and 37 seconds.

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 1 - ... is the angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle.

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 94 - 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 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 116 - 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...