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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 Excerpt:... in arithmetical progression: shew that the area is to that of an equilateral triangle having the same perimeter as May, 1869. 1. Explain what is meant by the circular measure of an angle. Why is it necessary to shew that the angle subtended at the centre of a circle by an arc equal to the radius is an invariable angle? Shew how to connect the circular measure of an angle with the measure of the same angle in degrees. The difference of two angles is 1; the circular measure of their sum is 1: find the angles. 2. Define the Trigonometrical Ratios. Shew that sinA + cosM = 1. Find the value of 0 from the equation Bin20-2cos0 + T = O. 4 Investigate the conditions which must hold in order that the equation sin20 + 6sin0 + c=O may have two admissible roots, or may have one. 3. Investigate the expressions for sin (A+B) and cos (A + B) in terms of the sines and cosines of A and B. Solve the following equations: (1) sin 30=8 sin2 0. (2) sin50=16sin60. 4. Find the sine and cosine of antangle of 18. Find the values of 0 between 0 and g-which satisfy the equation sin20 + coss20=7. 4 6. Define a logarithm. Explain the advantage of the common system of logarithms. Find approximately the value of x from the equation (ST---having given log 3 =-4771213. 7. Express the cosine of an angle of a triangle in terms of the sides. A person on the slope of a hill observes the angles of elevation a and /3 of two objects on the hill; and also the angle y which they subtend at his position: if 0 be the inclination of the hill to the horizon, shew that sin' 9 sin2 y=sin2 a+sinJ /3-2 sin a sin /3 cos y. 8. Shew how to solve a triangle, having given two sides and the included angle. If o=210, 6=110, C=34. 42'. 30", find the other angles, having given log 2=-3010300, icot 17. 21'. 15&q...