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. 1902 Excerpt: ...be constructed geometrically. 2. Assume values for N and n in the expression--and determine four angles, each less than 3, that can be constructed geometrically. Thus, let N=6, n = 3. Then, f-f = 45'. We shall now show how to find the functions of 3, and from them the functions of any multiple of 3. Since From either ...
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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. 1902 Excerpt: ...be constructed geometrically. 2. Assume values for N and n in the expression--and determine four angles, each less than 3, that can be constructed geometrically. Thus, let N=6, n = 3. Then, f-f = 45'. We shall now show how to find the functions of 3, and from them the functions of any multiple of 3. Since From either of these the other functions may be found. For the angle 18 let AB = x be the side of the regular inscribed decagon, and let AO = R (Fig. 42). Then, by geometry, R--x: x--x: R; whence, x--.. sin 18 =----=: AO 4 By successive applications of formulas (9) or (11) we can find the sine of the sum or difference of any two multiples of 3 whose sines and cosines have been previously found. Having found the sine and cosine of any angle in the series of multiples of 3, we may find the sine and cosine of half the angle by formulas (25) and (26). We may, therefore, find the sine, the cosine, and the other functions of any angle included in the form, given above. MISCELLANEOUS EXERCISES 1. Find the values of the following in the form of surds as above: cos 3, cos 33, sin 57, cos 6, sin 93, cos 12, sin 36, cos 7 30'. 2. Prove the relation P2 = H2 + D2, where P, H, D are the sides of the regular inscribed pentagon, hexagon, decagon respectively. D has been determined above; from a figure find P = 2 r sin 36. 3. Find the length of the side of the regular inscribed polygon of 60 sides in terms of the radius R. CHAPTER VIII RADIAN MEASURE, OR CIRCULAR MEASURE; INVERSE FUNCTIONS; GENERAL EXPRESSIONS 66. Radian Measure, or Circular Measure. To measure any magnitude is to find its ratio to some magnitude of the same kind taken as a unit. So, to measure an angle is to find its ratio to some constant angle taken as a unit. What the unit angle shall be, is enti...
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New. Trade paperback (US). Glued binding. 244 p. Contains: Illustrations, black & white. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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