A System of Plane and Spherical Trigonometry: To which is Added a Treatise on LogarithmsJ. & J.J. Deighton, 1831 - 330 Seiten |
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Seite 25
... results √3 2 sin 45 ° cos 45 ° = √2 tan 45 ° cot 45 ° = 1 . sec 45 ° cosec 45 ° = √2 . sin 30 ° cos 60 ° = } . cos 30 ° sin 60 ° = √3 2 tan 30 ° cot 60 ° cot 30 ° tan 60 ° = = 3 √3 7/3 sec 30 ° cosec 60 ° = 2 cosec 30 ° sec 60 ...
... results √3 2 sin 45 ° cos 45 ° = √2 tan 45 ° cot 45 ° = 1 . sec 45 ° cosec 45 ° = √2 . sin 30 ° cos 60 ° = } . cos 30 ° sin 60 ° = √3 2 tan 30 ° cot 60 ° cot 30 ° tan 60 ° = = 3 √3 7/3 sec 30 ° cosec 60 ° = 2 cosec 30 ° sec 60 ...
Seite 33
... , the result , as far as the decimal places agree in both , may be taken for an approximate value of π ; and , 96 therefore , by multiplying by 96 , π may be found . F 77. PROP . Tan a = ✓ G + cos PLANE TRIGONOMETRY . 33.
... , the result , as far as the decimal places agree in both , may be taken for an approximate value of π ; and , 96 therefore , by multiplying by 96 , π may be found . F 77. PROP . Tan a = ✓ G + cos PLANE TRIGONOMETRY . 33.
Seite 34
... Any arc whose cosine is known may be taken , and any integral value of n and π may be found in the same manner . The accuracy of the result will depend on the magnitude of n . .. sin 2 a = π 1 - ( tan 34 PLANE TRIGONOMETRY .
... Any arc whose cosine is known may be taken , and any integral value of n and π may be found in the same manner . The accuracy of the result will depend on the magnitude of n . .. sin 2 a = π 1 - ( tan 34 PLANE TRIGONOMETRY .
Seite 42
... be derived by similar pro- As there is not the least difficulty in the operations , a table of results has been deemed all that the student will find cesses . necessary . Values of sin 2 a . Values of cos 2 42 PLANE TRIGONOMETRY .
... be derived by similar pro- As there is not the least difficulty in the operations , a table of results has been deemed all that the student will find cesses . necessary . Values of sin 2 a . Values of cos 2 42 PLANE TRIGONOMETRY .
Seite 74
... result is m n m [ cosasin a ] = cos ( 2i - a ) ± √1 sin or , m m COS m n ( 2ix — a ) , m n [ cosa sin a ] " = cos ( 2in — a ) = √1 sin TM ( 2 i π — a ) . It must not be concluded from this that m COS 74 PLANE TRIGONOMETRY .
... result is m n m [ cosasin a ] = cos ( 2i - a ) ± √1 sin or , m m COS m n ( 2ix — a ) , m n [ cosa sin a ] " = cos ( 2in — a ) = √1 sin TM ( 2 i π — a ) . It must not be concluded from this that m COS 74 PLANE TRIGONOMETRY .
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Häufige Begriffe und Wortgruppen
A+B+C a+n ß a+ß a₁ B₁ base C₁ centre chord cosec cot cot diameter equal equations formula four right angles given greater or less hence hypothenuse integer intersection less than 90 Let the sides logarithm loge method Napier's rules nearly negative perpendicular plane angles plane triangle polar triangle pole PROB PROP quadrant quantity R₁ radius unity regular polyhedrons right-angled triangle Similarly sin A sin sin ß sines and cosines small circle solid angle sphere spherical angle spherical polygon spherical triangle ß₁ subtending sum the series suppose tangent trigonometric functions values vers α₁ Απ Δα ηβ π α π π
Beliebte Passagen
Seite 197 - IF two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz.
Seite 179 - The diameter of a sphere is any straight line which passes through the centre, and is terminated both ways by the superficies of the sphere.
Seite 190 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Seite 191 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Seite 181 - ... poles. 751. COR. 2. All great circles of a sphere are equal. 752. COR. 3. Every great circle bisects the sphere. For the two parts into which the sphere is divided can be .so placed that they .will coincide; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754.
Seite 252 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Seite 189 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 181 - An arc of a great circle may be drawn through any two points on the surface of a sphere.
Seite 45 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Seite 9 - The Versed Sine of an arc, is the part of the diameter intercepted between the arc and its sine.