Elementary Trigonometry: With a Collection of ExamplesDeighton, Bell, and Company, 1862 - 184 páginas |
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Página 15
... sin P'ON = = sin PON , r -b cos P'ON = cos PON , r tan P'ON == cosec P'ON = + p -tan PON , b r = cosec PON , p r sec P'ON = sec PON , -b -b cot P'ON = = -cot PON ; + p or we may write these results as follows : sin ( 180 ° -A ) = sin A ...
... sin P'ON = = sin PON , r -b cos P'ON = cos PON , r tan P'ON == cosec P'ON = + p -tan PON , b r = cosec PON , p r sec P'ON = sec PON , -b -b cot P'ON = = -cot PON ; + p or we may write these results as follows : sin ( 180 ° -A ) = sin A ...
Página 17
... sin A sin A S tan A = COS A ± √ ( 1 − sin2 A ) √ ( I - 82 ) ' I cot A = √ ( I - 82 ) == tan A Ꭶ I I sec A = cos A √ ( 1—82 ) › I I cosec A = sin A Wherever the double sign occurs before the radicals in these results , it arises ...
... sin A sin A S tan A = COS A ± √ ( 1 − sin2 A ) √ ( I - 82 ) ' I cot A = √ ( I - 82 ) == tan A Ꭶ I I sec A = cos A √ ( 1—82 ) › I I cosec A = sin A Wherever the double sign occurs before the radicals in these results , it arises ...
Página 19
... sin 30 ° I cot 30 ° = = tan 30 ° √3 , √3 sin 60 ° = sin ( 90 ° — 30 ° ) = cos 30 ° No3 , cos 60 ° = cos ( 90 ° — 30 ° ) = sin 30 ° = ; I 2 tan 60 ° = tan ( 90 ° -30 ° ) = cot 30 ° = √3 , and similarly , sec 60 ° = 2 , 2 cosec 60 ...
... sin 30 ° I cot 30 ° = = tan 30 ° √3 , √3 sin 60 ° = sin ( 90 ° — 30 ° ) = cos 30 ° No3 , cos 60 ° = cos ( 90 ° — 30 ° ) = sin 30 ° = ; I 2 tan 60 ° = tan ( 90 ° -30 ° ) = cot 30 ° = √3 , and similarly , sec 60 ° = 2 , 2 cosec 60 ...
Página 22
... sin and less than tan 0 . sin 0 tan 0 14. Limit of and of when is indefinitely diminished . We have proved in the last article that sin 0 , 0 , and tan 0 are in ascending order of magnitude ; therefore , di- viding each of them by sin 0 ...
... sin and less than tan 0 . sin 0 tan 0 14. Limit of and of when is indefinitely diminished . We have proved in the last article that sin 0 , 0 , and tan 0 are in ascending order of magnitude ; therefore , di- viding each of them by sin 0 ...
Página 25
... sin 90 ° = I. 2nd Quadrant , + p sin A = +2 , and is therefore positive ; r as A increases p decreases , and therefore sin A decreases in magnitude ; when A = 180 ° , p = 0 , and therefore sin 180 ° = 0 . 3rd Quadrant , sin A -p = r ...
... sin 90 ° = I. 2nd Quadrant , + p sin A = +2 , and is therefore positive ; r as A increases p decreases , and therefore sin A decreases in magnitude ; when A = 180 ° , p = 0 , and therefore sin 180 ° = 0 . 3rd Quadrant , sin A -p = r ...
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Términos y frases comunes
a+b+c a²+b² angle AOP angle of elevation angular arithmetical progression B-sin bisecting centre circular measure circumference circumscribing circle cos² cos³ cosec cosine decimal decreases in magnitude determined distance equal escribed circles EXAMPLES ILLUSTRATING CHAPTER feet Find the number find the value formula Given log given value Hence horizontal plane increases inscribed integer logarithm mount Ebal number of degrees number of grades Observe the angles perpendicular polygon Prove Quadrant quadrilateral radii radius regular polygon respectively revolving line right angle sec² secant secondary angle shew sides sign and magnitude similar triangles Similarly sin A sin sin A+B sin² sin³ sine sines and cosines Solve the equation solve the triangle straight line subtend tan² tangent tower triangle ABC trigono trigonometrical functions versin π π пп
Pasajes populares
Página 64 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 1 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 175 - ... 66. Construct an equilateral triangle, having given the length of the perpendicular drawn from one of the angles on the opposite side. 67. Having given the straight lines which bisect the angles at the base of an equilateral triangle, determine a side of the triangle. 68. Having given two sides and an angle of a triangle, construct the triangle, distinguishing the different cases. 69. Having given the base of a triangle, the difference...
Página 37 - B + cos A . sin B tan(A + B)= ) , (- = — . --. v cos (A + B) cos A . cos B — sin A . sin B and dividing numerator and denominator by cos A . cos B, sin A sin B cos A "'"cos B tan A + tan B 1 tan A.
Página 175 - Three circles are described, each of which touches one side of a triangle ABC, and the other two sides produced. If D be the point of contact of the side BC, E that of AC, and F that of AB, shew that AE is equal to BD, BF to CE, and CD to AF.
Página 5 - Now the angle at the centre of a circle which is subtended by an arc equal to the radius equals — = 57°. 29578, it so that the true length of a curve is given by the equation t IR L — ~ — — 57.2958 — 57.2958...
Página 113 - ... would be subtended at the centre of the first by an arc equal to the radius of the second. 9. If a be the arc which measures the complement of an angle to radius r, find the arc which measures the supplement of the same angle to radius r'.
Página 159 - It is required to bisect any triangle (1) bya line drawn parallel, (2) by a line drawn perpendicular, to the base. 43. To divide a given triangle into two parts, having a given ratio to one another, by a straight line drawn parallel to one of its...