Plane and Spherical TrigonometryGinn, 1890 - 245 Seiten |
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Seite 1
... Solution Case I. , when an acute angle and the hypotenuse are given , 16 ; Case II . , when an acute angle and the opposite leg are given , 17 ; Case III . , when an acute angle and the adjacent leg are given , 17 ; Case IV . , when the ...
... Solution Case I. , when an acute angle and the hypotenuse are given , 16 ; Case II . , when an acute angle and the opposite leg are given , 17 ; Case III . , when an acute angle and the adjacent leg are given , 17 ; Case IV . , when the ...
Seite 2
... solution of the isosceles spherical triangle , 116 ; solution of a regular spherical polygon , 116 . CHAPTER VI . THE OBLIQUE SPHERICAL TRIANGLE : Fundamental formulas , 117 ; formulas for half angles and sides , 119 ; Gauss's equations ...
... solution of the isosceles spherical triangle , 116 ; solution of a regular spherical polygon , 116 . CHAPTER VI . THE OBLIQUE SPHERICAL TRIANGLE : Fundamental formulas , 117 ; formulas for half angles and sides , 119 ; Gauss's equations ...
Seite 16
... logarithm or cologarithm , and is not written , it must be remembered that the logarithm or cologarithm is 10 too large . § 11. CASE II . Given A = 62 ° THE RIGHT TRIANGLE: Solution Case I , when an acute angle and the hypotenuse.
... logarithm or cologarithm , and is not written , it must be remembered that the logarithm or cologarithm is 10 too large . § 11. CASE II . Given A = 62 ° THE RIGHT TRIANGLE: Solution Case I , when an acute angle and the hypotenuse.
Seite 26
... solution gives the unknown parts of the polygon . h с Let , n = number of sides . c = length of one side . r = radius of circumscribed circle . h = radius of inscribed circle . p the perimeter . = F = the area . Then , by Geometry , F ...
... solution gives the unknown parts of the polygon . h с Let , n = number of sides . c = length of one side . r = radius of circumscribed circle . h = radius of inscribed circle . p the perimeter . = F = the area . Then , by Geometry , F ...
Seite 28
... solution of an oblique triangle , we now proceed to extend the definitions of the trigonometric functions to angles of all magnitudes , and to deduce certain useful relations of the functions of different angles . That branch of ...
... solution of an oblique triangle , we now proceed to extend the definitions of the trigonometric functions to angles of all magnitudes , and to deduce certain useful relations of the functions of different angles . That branch of ...
Häufige Begriffe und Wortgruppen
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 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 sin B sin sin² siny solution solve the triangle spherical triangle star subtended tan² tanc tangent tower Trigonometry unit circle vertical whence
Beliebte Passagen
Seite 51 - The sides of a triangle are proportional to the sines of the opposite angles.
Seite 109 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Seite 52 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Seite 53 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Seite 142 - 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°...
Seite 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 F the area...
Seite 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.
Seite 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.
Seite 70 - W., and after the ship had sailed 18 miles S. 67° 30' W. it bore N. 11° 15' E. Find its distance from each position of the ship. 2. Two objects, A and B, were observed from a ship to be at the same instant in a line bearing N. 15° E. The ship then sailed northwest 5 miles, when it was found that A bore due east and B bore northeast.
Seite 23 - From the top of a hill the angles of depression of two objects situated in the...