By George Salmon

Quantity: 2 writer: London Longmans, eco-friendly topics: Geometry, Analytic -- reliable Surfaces Notes: this is often an OCR reprint. there's typos or lacking textual content. There aren't any illustrations or indexes. for those who purchase the overall Books variation of this ebook you get loose trial entry to Million-Books.com the place you could make a choice from greater than 1000000 books at no cost. you can even preview the e-book there.

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**Extra info for A treatise on the analytic geometry of three dimensions**

**Example text**

4) ϭ 918 cm. C B 15 0 D E O 1 °M 22 2 1 ° 22 2 150 A H F G Fig. 12 To find the width of a river, a surveyor set up his surveying equipment at C on one bank and sighted across to a point B on the opposite bank; then, turning through an angle of 90Њ, he laid off a distance CA ϭ 225 m. Finally, setting the equipment at A, he measured / CAB as 48Њ20Ј. Find the width of the river. See Fig. 8. 1237) ϭ 253 m Fig. 13 In Fig. 9, the line AD crosses a swamp. In order to locate a point on this line, a surveyor turned through an angle 51Њ16Ј at A and measured 1585 feet to a point C.

Fig. 20 Obtain the trigonometric functions of 50Њ as in Prob. 19. Refer to Fig. 19. 7). 21 State the quadrant in which each angle terminates and the signs of the sine, cosine, and tangent of each angle. (a) 125Њ, (b) 75Њ, (c) 320Њ, (d) 212Њ, (e) 460Њ, (ƒ) 750Њ, (g) Ϫ250Њ, (h) Ϫ1000Њ Ans. 22 (b) I; ϩ, ϩ, ϩ; (f) I; ϩ, ϩ, ϩ; (c) IV; Ϫ, ϩ, Ϫ; (g) II; ϩ, Ϫ, Ϫ; (d) III; Ϫ, Ϫ, ϩ; (h) I; ϩ, ϩ, ϩ In what quadrant will u terminate if (a) (b) (c) (d) sin u and cos u are both positive? cos u and tan u are both positive?

As in Prob. 9, we bisect / AOB to form the right triangle MOB. 4) ϭ 918 cm. C B 15 0 D E O 1 °M 22 2 1 ° 22 2 150 A H F G Fig. 12 To find the width of a river, a surveyor set up his surveying equipment at C on one bank and sighted across to a point B on the opposite bank; then, turning through an angle of 90Њ, he laid off a distance CA ϭ 225 m. Finally, setting the equipment at A, he measured / CAB as 48Њ20Ј. Find the width of the river. See Fig. 8. 1237) ϭ 253 m Fig. 13 In Fig. 9, the line AD crosses a swamp.

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