Spherical Trigonometry ... |
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Page 30
... ; or else that the triangle has two quadrants and two right angles , and then the remaining side is equal to the remaining angle . α A 2 = 6. In an equilateral triangle , 30 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... ; or else that the triangle has two quadrants and two right angles , and then the remaining side is equal to the remaining angle . α A 2 = 6. In an equilateral triangle , 30 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Page 31
... equilateral triangle are restricted . 8. In an equilateral triangle , prove that sec A = 1 + sec a . 9. If the three sides of a spherical triangle be halved and b is given by cos 0 = cos 4 + a new triangle formed , the angle A b between ...
... equilateral triangle are restricted . 8. In an equilateral triangle , prove that sec A = 1 + sec a . 9. If the three sides of a spherical triangle be halved and b is given by cos 0 = cos 4 + a new triangle formed , the angle A b between ...
Page 66
... equilateral triangle tan R = 2 tan r . 7. If ABC be an equilateral spherical triangle , P the pole of the circle circumscribing it , Q any point on the sphere , shew that cos QA + cos QB + cos QC = 3 cos PA cos PQ . 8. If three small ...
... equilateral triangle tan R = 2 tan r . 7. If ABC be an equilateral spherical triangle , P the pole of the circle circumscribing it , Q any point on the sphere , shew that cos QA + cos QB + cos QC = 3 cos PA cos PQ . 8. If three small ...
Page 71
... equilateral triangle whose area is one - fourth of that of the sphere on which it is described . 2. Find the surface of an equilateral and equiangular sphe- rical polygon of n sides , and determine the value of each of the angles when ...
... equilateral triangle whose area is one - fourth of that of the sphere on which it is described . 2. Find the surface of an equilateral and equiangular sphe- rical polygon of n sides , and determine the value of each of the angles when ...
Page 82
... equilateral triangle ABC , and P any point upon the surface of the sphere , ( tan PO tan OA ) 3 ( cos PA + cos PB + cos PC ) 2 = cos2 PA + cos PB + cos PC - cos PA cos PB - cos PB cos PC - cos PC cos PA . 7. If ABC be a triangle having ...
... equilateral triangle ABC , and P any point upon the surface of the sphere , ( tan PO tan OA ) 3 ( cos PA + cos PB + cos PC ) 2 = cos2 PA + cos PB + cos PC - cos PA cos PB - cos PB cos PC - cos PC cos PA . 7. If ABC be a triangle having ...
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Common terms and phrases
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
Popular passages
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