Elements of Plane Trigonometry |
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12 read 9 Prop acute angle angle of elevation angle opposite antilogarithm cd L Ctn characteristic circle colog cologarithm column COMMON LOGARITHMS construct cos² cotangent Ctn c d d L Ctn d L Tan decimal point Denote determine digits divide draw equation EXAMPLE factors Find the angle Find the distance following triangles formulas given angle given number graph hence horizontal hypotenuse included angle law of cosines law of sines law of tangents Log10 Value Log10 Logo Value mantissa multiplications negative oblique triangles obtain obtuse angle perpendicular plane positive Pythagorean theorem quadrant radius ratios read as printed read co-function right triangle scale segment side adjacent side opposite sin² solution Solve subtends subtract tabular difference tan² tangent third side trigonometric functions Value Log10 Value Value Logo vertex vertical whence x-axis
Popular passages
Page 124 - The principles of their application are stated as follows : I. The logarithm of a product is equal to the sum of the logarithms of the factors : log ab = log a + log 6. This follows from the fact that if 10' = a and 101 = 6, l(f+L = a • b.
Page 125 - II. The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result. Thus, the characteristic of log...
Page 51 - 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 124 - The logarithm of the root of a number is found by dividing the logarithm of the number by the index of the root. For, \ Therefore, tag tfï = 2 = 6.
Page 125 - The logarithm of every number between 10 and 100 is some number between 1 and 2, ie, is 1 plus a fraction. The logarithm of every number between 100 and 1000 is some number between 2 and 3, ie, is 2 plus a fraction, and so on.
Page 125 - JVfor the first three digits and select the column headed by the fourth digit : the mantissa will be found at the intersection of this row and this column. Thus to find the logarithm of 72050, observe first (Rule I) that the characteristic is 4. To find the mantissa, fix attention on the digits 7205 ; find 720 in column X, and opposite it in column 5 is the desired mantissa, .85763 ; hence log 72050 = 4.85763.
Page 43 - Auxiliary Table of S and T for A in Minutes S = log sin A — log A' and T = log tan A — log A' For small angles: log sin A = log A' + S and log tan A = log A' + T. For angles near 90°: log cos A = log (90° — A...
Page 125 - RULE I. The characteristic of any number greater than 1 is one less than the number of digits before the decimal point. The...
Page 71 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.
Page 125 - PROBLEM 1. To find the logarithm of a given number. First, determine the characteristic, then look in the table for the mantissa. To find the mantissa in the table when the given number (neglecting the decimal point) consists of four, or less, digits (exclusive of ciphers at the beginning or end), look in the column marked N for the first three digits and select the column headed by the fourth digit : the mantissa will be found at the intersection of this row and this column. Thus to find the logarithm...