Elementary Trigonometry: With a Collection of ExamplesDeighton, Bell, and Company, 1862 - 184 páginas |
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Página 12
... sine , cosine and tangent are called the cosecant , secant and cotangent of A respectively . It is evident that the sine and cosine can neither of them exceed unity in magnitude , since the perpendicular and base are neither of them ...
... sine , cosine and tangent are called the cosecant , secant and cotangent of A respectively . It is evident that the sine and cosine can neither of them exceed unity in magnitude , since the perpendicular and base are neither of them ...
Página 15
... sine , tangent and secant of an angle are re- spectively the cosine , cotangent and cosecant of its com- plement . Again , draw OP ' making the same angle with ON ' which OP does with ON . Then the angle P'ON is the supplement of PON or ...
... sine , tangent and secant of an angle are re- spectively the cosine , cotangent and cosecant of its com- plement . Again , draw OP ' making the same angle with ON ' which OP does with ON . Then the angle P'ON is the supplement of PON or ...
Página 17
... sine , and therefore since the sine of the angle , and not the angle itself is given , we do not know of which of the angles corresponding to the same sine we are to take the cosine , tangent , cotangent , and secant respectively ; and ...
... sine , and therefore since the sine of the angle , and not the angle itself is given , we do not know of which of the angles corresponding to the same sine we are to take the cosine , tangent , cotangent , and secant respectively ; and ...
Página 18
... sine , cosine and tangent , the cases in which any one of them is given to determine the other tri- gonometrical functions from , are too simple to require special proof . 10. To find the trigo- nometrical functions of 30 ° and 60 ...
... sine , cosine and tangent , the cases in which any one of them is given to determine the other tri- gonometrical functions from , are too simple to require special proof . 10. To find the trigo- nometrical functions of 30 ° and 60 ...
Página 19
... and B is 45 ° ; .. sin 45 ° = AC = AC B AC I = = AB √ ( BC2 + AC2 ) = √ ( 2AC2 ) √ ( 2AC2 ) — √2 ' The cosine of 45 ° is evidently equal to the sine because BC = AC ; I .. cos 45 ° = √ / 2 AC 0 2 Functions of 30 ° , 60 ° , 45 ° . 19.
... and B is 45 ° ; .. sin 45 ° = AC = AC B AC I = = AB √ ( BC2 + AC2 ) = √ ( 2AC2 ) √ ( 2AC2 ) — √2 ' The cosine of 45 ° is evidently equal to the sine because BC = AC ; I .. cos 45 ° = √ / 2 AC 0 2 Functions of 30 ° , 60 ° , 45 ° . 19.
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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...