Trigonometry for Beginners with Numerous ExamplesMacmillan, 1868 - 200 sider |
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Side 17
... radius , describe a circle . Produce BO to meet the circum- ference at D. Draw PM perpendicular to OB ; and join PD . By Euclid III . 20 the angle PDM = ŁA . PM PM PM Now tan PDM = = DM ̄DO + OM ̄ ̄ ̄OP + OM ' Let OP - a ; then PM = sin ...
... radius , describe a circle . Produce BO to meet the circum- ference at D. Draw PM perpendicular to OB ; and join PD . By Euclid III . 20 the angle PDM = ŁA . PM PM PM Now tan PDM = = DM ̄DO + OM ̄ ̄ ̄OP + OM ' Let OP - a ; then PM = sin ...
Side 68
... B sin C sin A a = = b ; с and we shall shew hereafter that each of these is equal to 1 2R ' where R is the radius of the circle described round the triangle . 105. In any triangle ABC the tangent of half the 68 PROPERTIES OF TRIANGLES .
... B sin C sin A a = = b ; с and we shall shew hereafter that each of these is equal to 1 2R ' where R is the radius of the circle described round the triangle . 105. In any triangle ABC the tangent of half the 68 PROPERTIES OF TRIANGLES .
Side 69
... radius AB , describe a circle cutting AC at D. Produce CA to meet the circumference again at E. Draw DF at right angles to BD , meeting BC at F. The angle BAE is equal to the sum of the angles ABC and ACB , by Euclid 1. 32 ; the angle ...
... radius AB , describe a circle cutting AC at D. Produce CA to meet the circumference again at E. Draw DF at right angles to BD , meeting BC at F. The angle BAE is equal to the sum of the angles ABC and ACB , by Euclid 1. 32 ; the angle ...
Side 96
... and thus retains her in sight 40 minutes longer . Find the rate at which the ship is sailing , assuming the Earth to be a sphere of 4000 miles radius . 15. An observer from the deck of a ship 20 96 36 EXAMPLES . XII .
... and thus retains her in sight 40 minutes longer . Find the rate at which the ship is sailing , assuming the Earth to be a sphere of 4000 miles radius . 15. An observer from the deck of a ship 20 96 36 EXAMPLES . XII .
Side 97
... radius . 16. Two observers in the same horizontal plane sta- tioned at a distance of 200 yards from each other observed the altitude and bearing of the top of a tower ; to one of them the altitude was 60o bearing S. W. , and to the ...
... radius . 16. Two observers in the same horizontal plane sta- tioned at a distance of 200 yards from each other observed the altitude and bearing of the top of a tower ; to one of them the altitude was 60o bearing S. W. , and to the ...
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Trigonometry for Beginners, with Numerous Examples Isaac Todhunter Ingen forhåndsvisning tilgjengelig - 2010 |
Vanlige uttrykk og setninger
A-sin A+B+C Algebra angle increases angle PAB angles in terms angles included AP coincides AP moves Arithmetical Arithmetical Progression B-cos Cambridge centre circle circular measure circumference cloth cos² cos³ cosec cosine cotangent Crown 8vo decreases numerically determine distance draw PM perpendicular ELEMENTARY Euclid example expression Fcap feet figure find log find the height formulæ four right angles given angle Given log Hence hypotenuse increases from 180 inverse notation L sin logarithm Mathematical multiple of four negative and decreases number of degrees observe the angle opposite side plane positive angle preceding Article present Chapter quadrant PM regular polygon right-angled triangle sec² secant Second Edition shew sin A sin sin A+ sin sin sin sin² sin³ sine student suppose Tables tangent TREATISE Trigono Trigonometrical Ratios vers yards zero ОР
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