Plane Trigonometry for the Use of Colleges and Schools: With Numerous Examples

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Macmillan and Company, 1874 - Plane trigonometry - 341 pages

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Page 1 - Some angle is selected as the unit, and the measure of any other angle is the number of units which it contains. Any angle might be taken for the unit, as for example a right angle; but a smaller angle than a right angle is found more convenient. Accordingly a right angle is divided into 90 equal parts called degrees; and any angle may be estimated by ascertaining the number of degrees which it contains. If the angle does not contain an exact number of degrees we can express it in degrees and a fraction...
Page 18 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 37 - PM'is equal to AP ; thus as the angle increases from 0 to 90░ the sine increases from 0 to 1. While AP moves through the second quadrant PM is positive and continually decreases until AP coincides with AB; and then PM vanishes; thus as the angle increases from 90' to 180░ the sine diminishes from 1 to 0.
Page 94 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 35 - ... the sine of an angle is equal to the cosine of its complement, and the cosine of an angle is equal to the sine of its complement.
Page 95 - ... is some number between — 2 and — 3 ; that is, — 3 plus a fraction ; and so on. 5. In the common system, as the logarithms of all numbers which are not ^exact powers of 10 are incommensurable with those numbers, their values can only be obtained approximately, and are expressed by decimals. 6. The integral part of any logarithm is called the CHARACTERISTIC, and the decimal part is sometimes called the MANTISSA.
Page 178 - On the bank of a river there is a column 200 feet high, supporting a statue 30 feet high ; the statue to an observer on the opposite bank subtends the same angle as a man 6 feet high standing at the base of the column : find the breadth of the river.
Page 93 - The Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number. Thus if m = a", x is called the logarithm of m to the base a.
Page 2 - In this method a right angle is divided into 100 equal parts called grades, a grade is divided into 100 equal parts called minutes, and a minute is divided into 100 equal parts called seconds.

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