Plane and Spherical TrigonometryGinn & Company, 1892 - 166 σελίδες |
Άλλες εκδόσεις - Προβολή όλων
Plane and Spherical Trigonometry (Classic Reprint) G. A. Wentworth Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC Fig absolute value acute angle altitude angle of depression angle of elevation azimuth celestial sphere centre circle of latitude colog computed cos² cosb cosc cosecant cosine cosp cosx cosy cotangent cotx csc B csc denote ecliptic equal equation equinoctial EXAMPLE EXERCISE feet find the angles Find the area Find the distance Find the height Find the value Given Hence horizontal plane hour angle hypotenuse included angle isosceles Law of Sines Leaving latitude log csc logarithms longitude measured meridian miles moving radius Napier's Rules negative oblique observer obtain perpendicular pole positive ratios regular polygon right ascension right spherical triangle right triangle secant ship sails sin² sinx siny solution solve the triangle spherical triangle star subtended tan² tanc tangent tower trigonometric functions Trigonometry unit circle vertical whence
Δημοφιλή αποσπάσματα
Σελίδα 96 - V-- 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite to the side a, prove that 2 _ 8. Prove that in any plane triangle C* ~~i
Σελίδα 53 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Σελίδα 137 - Equinoctial, is the great circle in which the plane of the earth's equator produced intersects the surface of the celestial sphere.
Σελίδα 109 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Σελίδα 52 - The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle.
Σελίδα 100 - Assuming the formula for the sine of the sum of two angles in terms of the sines and cosines of the separate angles, find (i.) sin 75° ; (ii.) sin 3 A in terms of sin A.
Σελίδα 20 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and...
Σελίδα 142 - For (Fig. 50) the angle ZOB between the zenith of the observer and the celestial equator is obviously equal to his latitude, and the angle POZ is the complement of ZOB. The arc NP being the complement of PZ, it follows that the altitude of the elevated pole is equal to the latitude of the place of observation. The triangle ZPM then (however much it may vary in shape for different positions of the star M ) always contains the following five magnitudes : PZ= co-latitude of observer = 90°...
Σελίδα 23 - From the top of a hill the angles of depression of two objects situated in the...
Σελίδα 143 - ZM= zenith distance of star = z, PZM= azimuth of star = a, A very simple relation exists between the hour angle of the sun and the local (apparent) time of day. Since the hourly rate at which the sun appears to move from east to west is 15°, and it is Apparent noon when the sun is on the meridian of a place, it is evident that if hour angle = 0°, 15°, — 15°, etc., time of day is noon, 1 o'clock pM, 11 o'clock AM, etc. In general, if...