The Elements of Plane Trigonometry |
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a/sin acute angle b/sin broken line centre circle co-line computation congruent coördinates cos² cosecant cosine cotangent diedral difference directed lines distance draw equal equations face angles figure formula functions given horizontal hypotenuse ideal triangle initial line latitude law of cosines law of sines length log-sin logarithm longitude mantissa meridian miles minor projections negative normal opposite parallel perpendicular plane angle plane sailing plane triangle PLANE TRIGONOMETRY proj quadrant radians radius right angles right ascension right triangle right triangle ABC sailing secant segment side sin a sin sin² sine solution Solve species sphere spherical triangle subtended tangent terminal line theor tion triedral angle trigonometric functions trigonometric ratios values vertical
Popular passages
Page 50 - 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 112 - 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 167 - 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 131 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 7 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 7 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 64 - The sine of the difference of any two arcs or angles is equal to the sine of the first into the cosine of the second, minus the cosine of the first into the sine of the second.
Page 19 - 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 175 - To any observer the sensible horizon is a plane touching the earth's surface at the point of observation ; and a plane parallel to this plane through the earth's centre traces out on the celestial sphere the rational horizon, whose poles, zenith and nadir, are the traces of a vertical line, and whose secondaries are vertical circles. One of the vertical circles is also an hour-circle, the observer's celestial meridian, and passes through his zenith a'nd nadir, and the north and south poles of the...
Page 176 - ... 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 the star's longitude. 3. As to the horizon: The altitude of a star is its angular distance from the horizon measured on a vertical circle ; and the arc of the horizon intercepted between this circle and the south point of the horizon...