American book Company, 1909 - Plane trigonometry - 183 pages
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acute angles angle increases angle of elevation approaches becomes called circle coincide colog computation considered convenient corresponding cos x cosē cosh cosine cot 9 cotangent decreases definitions denominator determined difference directly distance divided draw employed equal equation example EXERCISE expression figures Find the value foot formulas four fraction Given greater ground height Hence increases length limit logarithm Ltan magnitude manner means measured method minute negative NOTE object observation obtained opposite Pages perpendicular plane positive problems Prove quadrant radians radius relations remaining respectively revolving line right triangle secē secant side similar sin x sinē sine sinh solution Solve subtended tanē tangent third tion tower trigonometric functions
Page 181 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 7 - If any three parts are given, one of them being a side, the other three can be found. The process of finding the unknown parts from the given parts is called the solution of the triangle.
Page 181 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 128 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 12 - A unit of plane angular measurement equal to the angle at the center of a circle subtended by an arc equal in length to the radius.
Page 11 - Every circumference is regarded as being divided into 360 equal parts, called degrees. Each degree is divided into 60 equal parts, called minutes, and each minute into 60 seconds. These divisions are indicated by the marks ° ' ". Thus 28 degrees, 17 minutes, and 49 seconds, are written 28° 17
Page 131 - Hence the Law of Tangents : The difference of two sides of a triangle is to their sum as the tangent of half the difference of the opposite angles is to the tangent of half their sum. NOTE.
Page 23 - A. p//// Hence it may be seen that the sine of an angle is the cosine of the complement of that angle; the tangent of an angle is the cotangent of its complement, and the secant of an angle is the cosecant of its complement. The functions of angles vary in sign according to the quadrant in which the angles are located. Let A A' and BB
Page 182 - The characteristic of the logarithm of a number greater than one is positive, and is one less than the number of digits in the integral part of the number.
Page 47 - ... angle of depression of the line of sight ? In the figure the height of the mountain is necessarily exaggerated. The angle is so small that the result can be found by five-place tables only between two limits which differ by 3' 40". 53. At a horizontal distance of 120 ft. from the foot of a steeple, the angle of elevation of the top is found to be 60° 30'.