The Elements of Plane and Spherical Trigonometry

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D. Appleton, 1879 - Trigonometry - 207 pages

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Page 54 - When the given angle is acute, and the side apposite the given angle is less than the other given side, and greater than the shortest dis.
Page 47 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 83 - In the circular measure of an angle and its intercepted arc, the unit of angle is an angle at the centre of a circle, subtended by an arc equal to the radius of the circle ; and this arc is the unit of arc.
Page 120 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 46 - For, since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO SIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES is to the TANGENT of HALF their DIFFERENCE.
Page 68 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles themselves.
Page 72 - Express the cosine of the difference of two angles in terms of the sines and cosines of these angles.
Page 85 - A = a ; that is, the circular measure of any angle, at the centre of a circle whose radius is unity, is equal to the length of the arc subtending that angle.

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