## Elements of Plane and Spherical Trigonometry: With Practical Applications |

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A B C acute angle angle equal angle opposite angle or arc APPLICATIONS ar.co.log base called characteristic circle complement corresponding cos² cosec Cosine Cotang decimal denoted determined difference distance divided draw equation EXAMPLES expressed feet figure formed formulæ Geom given gives greater half the sum height Hence horizontal hypothenuse included angle known latitude less log cos log cot log sin logarithmic sine manner means measured middle minus the logarithmic minutes Napier's rules negative object oblique oblique-angled spherical triangle observed obtain opposite perpendicular positive Prop quadrants ratios Required respectively right-angled triangle rods secant side sides equal sin A cos sin a sin sin² Solution solve the triangle spherical triangle Substituting subtract supplement taken Tang tangent tangent of half triangle equal trigonometric functions values whence yards

### Popular passages

Page 75 - 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...

Page 33 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.

Page 3 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant figure.

Page 43 - 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 85 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 46 - ... sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides, 117. Dividing (102) by (106), (103) by (107), and (104) by (108), we have, by (13...

Page 71 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.

Page 11 - ... multiplied by it will give a negative result ; but that which is to be carried from the decimal part will be positive; therefore, their difference will be the characteristic of the product. Ex. 1. Required the square, or second power, of 31. Log 31 = 1.491362 2 Ans. 961 2.982724 2. Required...