Elementary Trigonometry: With a Collection of ExamplesDeighton, Bell, and Company, 1862 - 184 páginas |
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Página 14
... those of its complement and supplement . Let PON be any angle A , of which the trigonometrical ratios are known . Then OPN is evi- dently its complement . P❜ Р N Now , ON sin OPN = ОР = cos PON 14 Complement and Supplement .
... those of its complement and supplement . Let PON be any angle A , of which the trigonometrical ratios are known . Then OPN is evi- dently its complement . P❜ Р N Now , ON sin OPN = ОР = cos PON 14 Complement and Supplement .
Página 50
... ( 45 ° -30 ° ) = sin 45 ° cos 30 ° -cos 45 ° sin 30 ° , cos 15 ° = cos ( 45 ° — 30 ° ) = cos 45 ° cos 30 ° + sin 45 ° sin 30 ° , and the sines and cosines of 45 ° and 30 ° are known . CHAPTER V. DETERMINATION , A PRIORI , OF THE NUMBER A A.
... ( 45 ° -30 ° ) = sin 45 ° cos 30 ° -cos 45 ° sin 30 ° , cos 15 ° = cos ( 45 ° — 30 ° ) = cos 45 ° cos 30 ° + sin 45 ° sin 30 ° , and the sines and cosines of 45 ° and 30 ° are known . CHAPTER V. DETERMINATION , A PRIORI , OF THE NUMBER A A.
Página 51
... known . If a be the circular measure of the least primary angle which has its cosine equal to cos A , any of the angles in- cluded in the formula 2nπ ± a will have its cosine equal to cos A. Hence , in finding the value of sin A from ...
... known . If a be the circular measure of the least primary angle which has its cosine equal to cos A , any of the angles in- cluded in the formula 2nπ ± a will have its cosine equal to cos A. Hence , in finding the value of sin A from ...
Página 67
... known . Then 10 " x N is a number with the same digits as N , but with the decimal point moved n places to the right , and N Ion is a number with the same digits as N , but with the decimal point moved n places to the left . Now log 10 ...
... known . Then 10 " x N is a number with the same digits as N , but with the decimal point moved n places to the right , and N Ion is a number with the same digits as N , but with the decimal point moved n places to the left . Now log 10 ...
Página 73
... known , we have , by substituting the three given values in these equations , three equations containing only three unknown quantities , and therefore we can , by solving the equations , find the values of the three remaining parts ...
... known , we have , by substituting the three given values in these equations , three equations containing only three unknown quantities , and therefore we can , by solving the equations , find the values of the three remaining parts ...
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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...