## Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of Computation, Volume 1 |

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addition algebraic angle applied axes base become called CHAPTER circle circumference co-ordinates completely compute consider corresponding cosec definition determined direction distance divided equal equations example EXERCISES expression figure fixed formulæ four functions geometry given gives height Hence included intersect latitude length limit measure metres multiplied negative NOTE obtain opposite parallel pass perpendicular plane polar triangle pole polygon positive powers preceding problem projection Prove quadrant quantities radius rectangular reduce relations remaining represented respective result right angle roots secant shown sides signs sin a cos sin a sin sine sines and cosines sinº Solution spherical triangle squares student substituting suppose tangent theorem third tion triangle trigonometric unit unity values

### Popular passages

Page 66 - 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 139 - 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 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 132 - 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 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.

Page 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.

Page 66 - IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle...

Page 105 - ... the modulus of a product is equal to the product of the moduli of the factors.

Page 43 - At the top of a tower, 108 feet high, the angles of depression of the top and bottom of...

Page 73 - The area of a triangle is equal to half the product of any two of its sides multiplied by the sine of the included angle, radius being unity.