Manual of Plane Trigonometry |
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angle ACB angle is equal Angles in terms angular unit Calculate the distance centre Chapter circular measure circumference complement cos² cos2A cosec cosine cot² cotangent coversin describe a circle diameter diff distances AC divided elevation equation Exercises feet find the angles Find the area find the distance formulæ given angle given side gles height Horizontal Plane hypotenuse included angle last proposition let fall log sin logarithmic miles nautical miles number of seconds Oblique-angled triangles observed obtain the following opposite angles plane triangle points quadrant radius required to express required to find right line right-angled triangle Sexagesimal sin A sin sin² sin²A sine sine and cosine single trigonometrical function Statement.-Let the angles station Substituting sum and difference tance tangent tion triangles BCP Trigono Trigonometrical Func twice an angle UNIVERSITY OF DUBLIN versin ов
Popular passages
Page 63 - Any three of these quantities which are independent being given, the remaining three may be found: this readily appears from the principles of geometrical construction. The three angles, A, B, C, are not independent, since their sum is equal to 1 80° ; and it is evident that an indefinite number of similar triangles may be constructed whose angles shall be equal respectively to three given angles, whose sum is 1 80°. If any other three of the six quantities, a, b, c, A, B, C, be given in numbers,...
Page 61 - ... lot which is laid out in a right-angled triangle, the base measuring 19 rods, and the perpendicular breadth 15 rods? Ans. 142.5. Case II. — To find the area of a triangle from the length of its sides. Rule. — 1. Add together the lengths of the three sides, and take half their sum. 2. From this half sum subtract each side separately. 3. Multiply together the half sum and each of the three remainders, and extract the square root of the product; the quotient will be the required area of the...
Page 55 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Page 36 - B (3) cos (A — B) = cos A cos B + sin A sin B (4) NOTE.
Page 36 - The tangent of the sum of two angles is equal to the sum of their tangents, divided by 1 minus the product of their tangents. 41 Sin (A - B), cos (A - B), AND tan (A - B) If A and B are any two angles then, sin (A — B) = sin A cos B — cos A...
Page 86 - To the height of the eye in feet add half the height, and extract the square root of the sum; the result will be the distance in statute miles.
Page 6 - There are thus 2тг, or approximately 6'283, radians in one complete revolution. Generally, the angle between two lines meeting at the centre of a circle is equal to the ratio of the length of arc between the two lines to the radius of the circle. circular mil (Kite.