A Treatise on TrigonometryFinch & Apgar, 1881 - 102 pàgines |
Altres edicions - Mostra-ho tot
A Treatise on Trigonometry James Edward Oliver,George William Jones,Lucian Augustus Wait Visualització completa - 1883 |
Frases i termes més freqüents
a+b+c abscissa angle or arc circle circumscribed circle computation cosb cosc cosecant cosine cosp cos q cot Q cotangent cotp cotq csc0 determined without ambiguity differs from 90 distance formulae of Thm fourth quadrant geom Given two sides greater than 90 half the perimeter hypothenuse less than 90 let xop logarithmic sines nearer 90 nearer to 90 negative angle negative with reference NOTE oblique angle oblique triangles opposite angle ordinate perpendicular plane triangle ABC positive or negative possible errors PROB prop'n radius ratios reader may prove right angle right spherical triangle right triangles secant sin a sin sin s-c sin0 sin³0 sinb sinc sine sine and cosine sinp sinq spherical triangle ABC spherical trigonometry supplement tana tanc tangent tano theorem trigonometric functions TRIGONOMETRY values whence wherein
Passatges populars
Pàgina 47 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Pàgina 65 - N. by E. NNE NE by N. NE NE by E. ENE E. by N. East E. by S. ESE SE by E. SE SE by S.
Pàgina 73 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B...
Pàgina 60 - From half the sum of the sides subtract each side separately. Multiply the half sum and the several remainders together, and the square root of the product will be the area.
Pàgina 10 - The sine is positive in the first and second quadrants, and negative in the third and fourth : • 2d.
Pàgina 75 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Pàgina 65 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Pàgina 64 - Ex. 18. 1. At 120 feet distance from the foot of a steeple, the angle of elevation of the top was found to be 60° 30'.
Pàgina 69 - , i tan b whence, cos A = tan c In a similar way the other relations in (l)-(6) can be shown to be true for ABC (Fig. 28). 27. On species. Two parts of a spherical triangle are said to be of the same species (or of the same affection) when both are less than 90°, both greater than 90°, or both equal to 90°. Formula (1), Art. 26, shows that the hypotenuse of a right-angled spherical triangle is less than 90° when the sides about the right angle are both greater or both less than 90° ; and it...
Pàgina 59 - For the area, multiply half the product of any two sides by the sine of the included . angle.