## Plane TrigonometryPlane Trigonometry by James Morford Taylor, first published in 1904, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |

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### Common terms and phrases

acute angle Algebra angle angle of elevation arithmetic base called changes CHAPTER Check circle complex number compute Construct cosē cosh cosine coterminal curve denote difference directed line Dividing draw equal equation examples EXERCISE Express figure Find Find the distance force formulas four functions Given half Hence horizontal identities includes increases length loga logarithms measure Multiplying Observe obtain opposite plane positive principal value Prove Putting quadrant quality unit radians radius reciprocal regular relations represented respectively resultant right triangles roots secē ship sides sinē sine sinh solution Solve Substituting Take tanē tangent third tower triangle triangle ABC trigonometric ratios vector ηπ

### Popular passages

Page 75 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.

Page 140 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively. Prove that the length of the pole is twice the height of the mound.

Page 78 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.

Page 16 - DB which stands on a horizontal plane. From a point A on this plane he finds the angle of elevation of the top of the tower to be .35°.

Page 18 - A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 50° ; walking 40 ft.

Page 127 - The modulus of the quotient of two complex numbers is equal to the quotient of their moduli.

Page 19 - ... down it is 28°. The inclination of the plane is 7°. Find the height of the tower. 10. From the top and bottom of a castle which is 75 ft high the angles of depression of a ship at sea are 19° and 15° respectively. Find the distance of the ship from the bottom of the castle. 11. A monument 70 ft. high and a tower stand on the same horizontal plane. The angle of elevation of the top of the tower at the top of the monument is 20° 40' 12" [20.67°], at the base of the monument it is 53° 31'...

Page 88 - ... and the shorter diagonal is 16 ft. Find the area. 189. The acute angles of a rhombus are each equal to 60°, and the longer diagonal is 108 yds. Find the area. 190. Two vessels start at the same time from the same place, and sail, one due north, the other due east, at the rates of 6 and 8 mi. per hour respectively. How far apart will they be at the end of 6 hrs. ? 191. What distance will a man save, if, instead of walking along the sides of a rectangular field 640 yds. long and 480 yds. wide,...

Page 65 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 22 - ... expect wet and stormy weather. These two types of weather correspond respectively to a condition of high atmospheric pressure or anticyclone and a state of low atmospheric pressure or cyclone. The winds in a cyclone are often strong and swirl round the centre of lowest pressure in great spirals with a direction opposite to that of the hands of a clock. When anticyclonic conditions prevail, the winds are light and move round the area of highest pressure in the same direction as the hands of a...