Plane and Spherical Trigonometry |
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absolute value acute angle adjacent altitude angle of depression angle of elevation azimuth circular measure colog cologarithm computed cos² cosb cosc cosecant cosp cosx cosy cotangent cotx denote departure equal equation equinoctial EXAMPLE EXERCISE feet Find the angle Find the area Find the distance Find the height Find the value formulas functions Hence horizontal plane hour angle hypotenuse included angle inscribed isosceles Law of Sines log cos 9 log cot log log csc log sec log tan log logarithm longitude mantissa meridian miles moving radius Napier's Rules negative oblique observer obtain pole positive Prove ratios regular polygon required number right spherical triangle right triangle secant ship sails siny solution solve the triangle spherical triangle star subtended tan² tanc tangent tower trigonometric functions Trigonometry unit circle vertical whence
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Page 140 - For (Fig. 46) 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°...
Page ii - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Page 51 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 50 - 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.
Page 98 - 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.
Page 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...
Page 107 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 72 - At a distance a from the foot of a tower, the angle of elevation A of the top of the tower is the complement of the angle of elevation of a flagstaff on top of it. Show that the length of the staff is 2 a cot 2 A.
Page 50 - 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.
Page 21 - From the top of a hill the angles of depression of two objects situated in the...