The Elements of Plane Trigonometry |
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Common terms and phrases
A+ cot a+b+c AB² AC² angle ACB angle of elevation AO² AP AP Asin B-cos BC² BOP₁ centre circumference circumscribed cos A cos cos¹ cos² cos³ cosine cot A cot cot A+ cot² OPA cot³ diameter distance Divide equal equation feet formula given height hence hexagon inscribed circle logarithms negative nth root number of sides OA cot OB² perimeter perpendicular plane triangle quadrant r² cot radii radius ratio regular polygon right angle right-angled triangle sec² sector shew sin A cos sin A sin sin-¹ sin¹ sin² sin² 18 sin³ sine and cosine square subtend subtracted tan-¹ tan² tan³ tangent triangle ABC Trigonometry unity values
Popular passages
Page 101 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.
Page 102 - Wanting to know my distance from an- inaccessible object 0, on the other side of a river ; and having no instrument for taking angles, but only a chain or cord for measuring distances ; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to 100 yards ; also the diagonal AD measured 550 yards, and the diagonal BC 560.
Page 91 - The square on the side of a regular pentagon inscribed in a circle is equal to the sum of the squares on the sides of the regular hexagon and decagon inscribed in the same circle.
Page 101 - I took the angle of elevation of the top of the hill 40°, and of the top of the tower 51°; then measuring in a line directly from, it to 'the distance of 200 feet farther, I found the angle to the top of the tower to be 33° 45'.
Page 101 - ... to be on a level with the place where I st.ood, close by the side of the river; and not having room to measure backward...
Page 100 - A point of land was observed, by a ship at sea, to bear east-by-south ; and after sailing north-east 12 miles, it was found to bear south-east-by-east. It is required to determine the place of that headland, and the ship's distance from it at the last observation ? Ans.
Page 36 - Since the cosine of any angle is equal to the sine of its complement,. cos 54 = sin 36, but cos 54 = cos (36 + 18) = cos 36 cos 18 - sin 36 sin 18 ; .". cos 36 cos 18 - sin 36 sin 18 = sin 36, but cos 36 = 1 - 2 sin' 18, and sin 36' = 2 sin 18 cos 18"; .". cos 18 (1-2 sin' 18) - 2 sin