Elementary Trigonometry |
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Page 6
... perpendicular to AQ . Thus a right - angled triangle BAC is formed . With reference to the angle A the following definitions are em- ployed . BC opposite side hypotenuse The ratio or AB AC The ratio or AB BC The ratio or AC AC The ratio ...
... perpendicular to AQ . Thus a right - angled triangle BAC is formed . With reference to the angle A the following definitions are em- ployed . BC opposite side hypotenuse The ratio or AB AC The ratio or AB BC The ratio or AC AC The ratio ...
Page 9
... perpendicular to OA . Also take any point Fin OP and draw FG at right angles to OP . From the triangle BOC , sin POA = BC OB from the triangle DOE , sin POA : = DE OD ' FG from the triangle FOG , sin POA - OG But the triangles BOC , DOE ...
... perpendicular to OA . Also take any point Fin OP and draw FG at right angles to OP . From the triangle BOC , sin POA = BC OB from the triangle DOE , sin POA : = DE OD ' FG from the triangle FOG , sin POA - OG But the triangles BOC , DOE ...
Page 10
... perpendicular to BC and meets CA produced in D : if AB = 12 , AC = 16 , BC = 20 , find BD and CD . From the right - angled tri- angle CBD , BD = tan C ; BC from the right - angled triangle ABC , AB tan C ; AC 20 12 16 A BD BD BC = = AB ...
... perpendicular to BC and meets CA produced in D : if AB = 12 , AC = 16 , BC = 20 , find BD and CD . From the right - angled tri- angle CBD , BD = tan C ; BC from the right - angled triangle ABC , AB tan C ; AC 20 12 16 A BD BD BC = = AB ...
Page 14
... perpendicular to a AC , and denote the sides of the right - angled triangle ABC by a , b , c . and By definition , sin A = cos A = BC AB AC AB α = - = с b с a2 = 212 b2 a2 + b2 ... sin2 A + cos2 A = = 1 . COR . sin2 A = 1 - cos2 A , sin ...
... perpendicular to a AC , and denote the sides of the right - angled triangle ABC by a , b , c . and By definition , sin A = cos A = BC AB AC AB α = - = с b с a2 = 212 b2 a2 + b2 ... sin2 A + cos2 A = = 1 . COR . sin2 A = 1 - cos2 A , sin ...
Page 38
... perpendicular from C upon AB produced . Draw CD perpendicular to AB produced , and let CD = x . Then CBD = 180 ° - 135 ° 45 ° ; .. BD = CD = x . Now in the right - angled tri- angle ADC , CD AD that is , = tan DAC = tan 30 ° ; Ꮖ . = 1 ...
... perpendicular from C upon AB produced . Draw CD perpendicular to AB produced , and let CD = x . Then CBD = 180 ° - 135 ° 45 ° ; .. BD = CD = x . Now in the right - angled tri- angle ADC , CD AD that is , = tan DAC = tan 30 ° ; Ꮖ . = 1 ...
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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...