Elementary Trigonometry |
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Page 1
... posi- tion OA before taking up its final position . H. K. E. T. 1 It will thus be seen that in Trigonometry angles are Chapter I MEASUREMENT OF ANGLES Definition of Angle Chapter VARIATIONS OF THE FUNCTIONS Definition of limit.
... posi- tion OA before taking up its final position . H. K. E. T. 1 It will thus be seen that in Trigonometry angles are Chapter I MEASUREMENT OF ANGLES Definition of Angle Chapter VARIATIONS OF THE FUNCTIONS Definition of limit.
Page 50
... taking n sufficiently large we can make the perimeters of the two polygons differ from the circumferences of the corresponding circles by as small a quantity as we please ; so that ultimately C1 C2 21 where € 1 and c2 are the ...
... taking n sufficiently large we can make the perimeters of the two polygons differ from the circumferences of the corresponding circles by as small a quantity as we please ; so that ultimately C1 C2 21 where € 1 and c2 are the ...
Page 55
... Taking π = find the radian measure of : 7 ' 23. 36 ° 32 ′ 24 ′′ . 24. 70 ° 33 ′ 36 ′′ . 25. 116 ° 2 ' 45′6 ′′ . · 26. 171 ° 41 ' 50.4 " . 27. Taking 1 π = = 31831 , shew that a radian contains 206265 seconds approximately . 28. Shew ...
... Taking π = find the radian measure of : 7 ' 23. 36 ° 32 ′ 24 ′′ . 24. 70 ° 33 ′ 36 ′′ . 25. 116 ° 2 ' 45′6 ′′ . · 26. 171 ° 41 ' 50.4 " . 27. Taking 1 π = = 31831 , shew that a radian contains 206265 seconds approximately . 28. Shew ...
Page 60
... taking π = and the earth's diameter as 7920 miles . י 7 12. Find the radius of a globe such that the distance measured along its surface between two places on the same meridian whose latitudes differ by 13 ° may be 1 foot , taking = 22 ...
... taking π = and the earth's diameter as 7920 miles . י 7 12. Find the radius of a globe such that the distance measured along its surface between two places on the same meridian whose latitudes differ by 13 ° may be 1 foot , taking = 22 ...
Page 61
... Taking = find the sexa- gesimal measure of the angle . 10 . 2 7 If B = 30 ° , C = 90 ° , b = 6 , find a , c , and the perpendicular from C on the hypotenuse . 11. Shew that π ( 1 ) cot 0 + cot ( 1 - 0 ) cosec cosec ( 2 ) cosec2 + cosec2 ...
... Taking = find the sexa- gesimal measure of the angle . 10 . 2 7 If B = 30 ° , C = 90 ° , b = 6 , find a , c , and the perpendicular from C on the hypotenuse . 11. Shew that π ( 1 ) cot 0 + cot ( 1 - 0 ) cosec cosec ( 2 ) cosec2 + cosec2 ...
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Common terms and phrases
1+cos 1+tan² a+cos a+sin a+ß A+tan acute angle angle of elevation B+cos centre circle cos A cos cos² cos³ cosec cosine cot² cyclic quadrilateral decimal denote diff equal equation ex-central triangle Example expression feet Find the angle find the distance find the height Find the number Find the value flagstaff following identities formula fraction given log greatest angle Hence horizontal plane hypotenuse integer loga magnitude mantissa miles negative number of radians obtain pedal triangle perpendicular positive Prove the following quadrant quadrilateral quantities radian measure radius vector regular polygon right angle right-angled triangle sec² sexagesimal shew sin A sin sin sin sin sin² sin³ sine solution solve the triangle supplementary angles tan² tangent tower triangle ABC trigonometrical functions trigonometrical ratios whence Зп
Popular passages
Page 131 - ... the logarithm of a fraction is equal to the logarithm of the numerator diminished by the logarithm of the denominator...
Page 179 - From a station, B, at the base of a mountain, its summit A is seen at an elevation of 60° ; after walking one mile towards the summit, up a plane making an angle of 30° with the horizon, to another station, C, the angle BCA is observed to be 135° : find the height of the mountain in yards.
Page 350 - OF EUCLID'S ELEMENTS. Including Alternative Proofs, together with additional Theorems and Exercises, classified and arranged. By HS HALL, MA, and FH STEVENS, MA, Masters of the Military and Engineering Side, Clifton College. Gl.
Page 132 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Page 39 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius of the circle...
Page 132 - Let N be a number whose integral part contains n digits ; then JV= JQ<il>HftiMlon . .'. log^V=(?t— l) + a fraction. Hence the characteristic is и — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and is positive.
Page 187 - From the top of a hill the angles of depression of two objects situated in the...
Page viii - ... equal parts, called degrees; a degree into 60 equal parts, called minutes; a minute into 60 equal parts, called seconds. Degrees, minutes, and seconds are indicated in connection with numbers by the respective symbols °, ', ". 25 degrees, 18 minutes, 34 seconds is written 25° 18
Page xi - Ratio is the relation which one quantity bears to another of the same kind, with reference to the number of times that the one is contained in the other.
Page 348 - We will not say that this is the best Elementary Algebra for school use that we have come across, but we can say that we do not remember to have seen a better. . . . It is the outcome of a long experience of schoolteaching, and so is a thoroughly practical book. All others that we have in our eye are the works of men who have had considerable experience with senior and junior students at the universities, but have had little...