A Treatise on TrigonometryFinch & Apgar, 1881 - 102 sider |
Andre utgaver - Vis alle
A Treatise on Trigonometry James Edward Oliver,George William Jones,Lucian Augustus Wait Uten tilgangsbegrensning - 1883 |
Vanlige uttrykk og setninger
a+b+c abscissa angle or arc circle circumscribed circle computation cosb cosc cose cosecant cosine cosp cos q cot Q cotangent cotc cotp cotq cotr csc0 determined without ambiguity differs from 90 distance equal formulae of Thm fourth quadrant geom Given two sides greater than 90 half the perimeter hypothenuse initial line less than 90 let xop nearer 90 negative angle NOTE oblique angle oblique triangles obtuse opposite angle ordinate P₂ perpendicular positive or negative possible errors PROB q'+q radius ratios reader may prove reference to ox revolution right angle right spherical triangle right triangles sec0 secant second quadrant sin a sin sine sine and cosine sinp spherical triangle ABC spherical trigonometry supplement tanc tangent tanp cotp terminal line theorem trigonometric functions values whence wherein
Populære avsnitt
Side 37 - 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.
Side 63 - 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 sin C...
Side 50 - 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.
Side 62 - ABC ; then'.' cos A = cos a sin B, and sin B is positive, .'. cos A, cos a are positive, negative, or zero together, .'. A, a are both acute, both obtuse, or both right. QED THEOR. 21. In an ideal right triangle, if the hypotenuse be acute the two oblique sides are of the same species, and so are the two oblique angles ; but they are of opposite species if the hypotenuse be obtuse. For let c be the right angle in the triangle ABC ; then'.
Side 36 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Side 55 - 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.