## The Essentials of Plane and Spherical Trigonometry |

### From inside the book

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**denoting**the sides BC , CA , and AB by a , b , and c , and employing the usual abbreviations , sin A α = 19 tan A a = sec A = с b b b ( 1 ) cos A с == cot A csc A = с α And in like manner , sin B COS B b 4 PLANE TRIGONOMETRY . THE ... Page 73

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**Denoting**the area by K , we have by Geometry , 2 K = ab . But by Art . 13 , a = csin A , and b = c cos A. Whence , That is , 2K c2 sin A cos Ac2 sin 24 ( Art . 74 ) . = 4 K = c2 sin 2 A. = In like manner , = 4K c2 sin 2 B. ( 36 ) ( 37 ) ... Page 79

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**Denoting**a + b + c by 2s , so that s is the half - sum of the sides of the triangle , we have and ab + c = ( a + b + c ) -2b = 2s - 2b - 2 ( s — b ) , a + b - c = ( a + b + c ) -2c = 2s - 2c = 2 ( s - c ) . Hence , sin2 4 = 4 ( s — b ) ... Page 81

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**denoting**the area of the triangle by K , we have by Geometry , 2K cx CD . = But in Fig . 1 , sin 4 = CD , A b and in Fig . 2 , = sin A sin ( 180 ° - CAD ) CD = sin CAD ( Art . 47 ) = b Whence , in either figure , CD = b sin A. Therefore ... Page 86

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**Denoting**= - ( s − a ) ( s — b ) ( s − c ) s - a s ( s - a ) 2 ( sa ) ( s — b ) ( s — c ) ( s − a ) ( s — b ) ( s — - c ) S by r , we have Ꭶ r tan4 = s - a In like manner , r r tan B = and tanC = • 9 S- · b ' S - C 1. Given a 2.5 ...### Other editions - View all

### Common terms and phrases

A'BC abscissa acute angle adjacent angle corresponding angle obtained C₁ CD² check formula circular measure colog cologarithm cos a cos cos(x+y cos² cosecant cosine cotangent decimal Denoting distance equal EXAMPLES find the angle find the logarithm find the values following triangles formulæ of Art functions Geometry given elements Given the three Given two sides Hence hypotenuse included angle log cot log csc log sin log tan manner mantissa Napier's rules Note obtain the formulæ opposite angle ordinate perpendicular polar triangle positive radius right angle right triangle ABC secant sin B sin sin C cos sin² Solve the following spherical oblique triangles spherical right triangle spherical triangle Spherical Trigonometry subtract tanc tangent terminal line triedral angle trigonometric functions Trigonometry Whence by Art XOP₁ ос

### 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...