Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students |
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Page 284
... cosine , and co- tangent of obtuse angles are negative , while the sine and cosecant of obtuse angles are positive . For , when the revolving line is in the second quarter of its revolution , that is , between AY and AX ' , the side AC ...
... cosine , and co- tangent of obtuse angles are negative , while the sine and cosecant of obtuse angles are positive . For , when the revolving line is in the second quarter of its revolution , that is , between AY and AX ' , the side AC ...
Page 285
... cosine is - ANGLES OF A GIVEN FUNCTION . 828. Theorem . — Any given simple function , when taken irrespective of its algebraic sign , belongs to four different angles within each revolution . B If BAC is the acute angle of a given ...
... cosine is - ANGLES OF A GIVEN FUNCTION . 828. Theorem . — Any given simple function , when taken irrespective of its algebraic sign , belongs to four different angles within each revolution . B If BAC is the acute angle of a given ...
Page 286
... cosine and secant of an angle and of its negative have the same signs , while the other simple functions of such angles have opposite signs . The tangent and cotangent of an angle , and of the same angle increased by two right angles ...
... cosine and secant of an angle and of its negative have the same signs , while the other simple functions of such angles have opposite signs . The tangent and cotangent of an angle , and of the same angle increased by two right angles ...
Page 287
... cosine are fractions having the numerator less than the denominator . 833. Theorem . - The secant and cosecant can ... cosine of 0 ° is 1 , which decreases as the angle increases till the cosine of 90 ° is 0 , and the cosine of - 180 ...
... cosine are fractions having the numerator less than the denominator . 833. Theorem . - The secant and cosecant can ... cosine of 0 ° is 1 , which decreases as the angle increases till the cosine of 90 ° is 0 , and the cosine of - 180 ...
Page 288
... cosine and secant of - 450 ° ? 4. What are the cosecant and cotangent of 150 ° ? 5. Construct an angle greater than 90 ° , whose sine is one whose tangent is ; one whose cosine is RELATIONS BETWEEN THE FUNCTIONS . 836. A simple function ...
... cosine and secant of - 450 ° ? 4. What are the cosecant and cotangent of 150 ° ? 5. Construct an angle greater than 90 ° , whose sine is one whose tangent is ; one whose cosine is RELATIONS BETWEEN THE FUNCTIONS . 836. A simple function ...
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Common terms and phrases
adjacent angles altitude angles equal apothem axis base bisect chord circle circumference circumscribed coincide cone Corollary Corollary.-The cosine Cotang curved surface cylinder demonstrated diagonals diameter dicular diedral angles diedral whose edge distance divided draw equal angles equally distant equivalent faces figure formula four right angles frustum functions Geometry given angle given line given point given straight line given triangle gles greater Hence homologous lines hypotenuse included angle inscribed intersection Join less let fall logarithm mantissa number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular polyedral prism Problem.-Given proportional pyramid quadrilateral radii radius ratio regular polygon respectively equal right angled triangle secant similar similarly arranged sine slant hight sphere spherical excess spherical polygon spherical triangle square student subtracting symmetrical Tang tangent tetraedrons theorem Theorem.-The triedral vertex vertices
Popular passages
Page 98 - If two triangles have two sides of the one equal to two sides of the...
Page 182 - ... the plane at equal distances from the foot of the perpendicular, are equal...
Page 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Page 84 - If a circle have any number of equal chords, what is the locus of their points of bisection? 21. If any point, not the center, be taken in a diameter of a circle, of all the chords which can pass through that point, that one is the least which is at right angles to the diameter. 22. If from any point there extend two lines tangent to a circumference, the angle contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them....
Page 117 - ABC, so that DE shall be equal to the difference of BD and CE. 22. In a given circle, to inscribe a triangle similar to a given triangle. 23. In a given circle, find the locus of the middle points of those chords which pass through a given point. 25. If a line bisects an exterior angle of a triangle, it divides the base produced into segments ^A which are proportional to the adjacent sides.
Page 307 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 237 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 233 - The volume of a rectangular parallelepiped is equal to the product of its three dimensions.
Page 126 - Theorem. — Two parallelograms are equal when two adjacent sides and the included angle in the one, are respectively equal to those parts in the other.