## A Drill-book in Trigonometry |

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a/sin acute angle area swept axis biquadrantal broken line celestial sphere centre circle co-line computed cos2a cosb cosc cose cosecant cosine cotangent Delambre's formulas departure difference of latitude difference of longitude directed lines draw ecliptic equal equations exterior angles face angles feet figure given horizontal hour-angle hypotenuse ideal triangle initial line law of cosines law of sines length log-sin log-tan logarithms maj-proj mantissa miles minor projections motion nearer right negative normal to ox oblique triangle obtuse opposite parallel perpendicular plane angle plane sailing plane triangle positive and less positive end possible errors proj quarter radians radius right angles right ascension right triangle abc sailing secant segment sides signs sinb sine solution Solve species spherical triangle subtended sun's swinging tana tangent terminal line theor theorem triedral angle trigonometric ratios trigonometry values

### Popular passages

Page 48 - A a = sin (a + 2) sin a cos sin (a + ft) = sin a cos ft + cos a sin ft sin (a — ft) = sin a cos /? — cos a sin /? cos (a + ft) = cos a cos ft — sin a sin ft...

Page 110 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.

Page 174 - ... the star's hour-circle, and is counted from the meridian, positive towards the west and negative towards the east. The right ascension of a fixed star changes very little, since the vernal equinox is nearly fixed on the celestial sphere ; the hour-angle changes every moment. 2. As to the ecliptic: The latitude of a star is its angular distance from the ecliptic measured on a secondary ; and the arc of the ecliptic intercepted between the vernal equinox and this secondary, measured eastward, is...

Page 165 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 60 - EXAMPLES. 1. Show directly from the definitions what are the largest and what the smallest values that each function may have, and state for what angles the several functions take these values. 2. Draw the curve of tangents, curve of secants, curve of cosines, curve of cotangents, and curve of cosecants.

Page 17 - 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?

Page 125 - Formeln berechnen: sin a/sin a = sin 6/sin /? = sin c/sin y cos a = cos b cos c + sin b sin c cos a cos b = cos c cos a + sin c sin a cos...

Page 18 - Definitions. The LATITUDE of a point is its distance North or South of some " Parallel of Latitude," or line running East or West.

Page 17 - ... find the earth's diameter, and the distance of the sea-horizon. 7. What is the distance and the dip of the sea-horizon from the top of a mountain 2J miles high, the earth's mean radius being 3956 miles ? [2° 8

Page 154 - A biquadrantal triangle is indeterminate unless either the base or the vertical angle be given. ISOSCELES TRIANGLES. Draw an arc from the vertex to the middle of the base, thereby dividing the given triangle into two equal right triangles; solve one of these triangles. If only the base and the vertical angle be given, there are two triangles, one triangle, or none, according as the base is less than, equal to, or greater than the vertical angle ; if only the two equal sides or the two equal angles...