## An elementary treatise on plane trigonometryMacmillan, 1858 - 106 pages |

### From inside the book

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**revolving line**OP , that is , as 180 ° + A'OP ̧ · So also when the**revolving line**reaches OP , the Trigonome- trical angle AOP will be 270 ° + B'OP ; and when OP has passed its initial position OA and reached OP , a second time , the ... Page 6

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**revolving line**OP ( fig . Art . 7 ) have come into any position OP1 , OP ,, .... , and from P1 , P ,, .... , drop the perpendiculars PN , PM , .... upon the initial line OA , or OA produced backwards to A ' ; the triangles PNO , PMO ... Page 8

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**revolving line**. So also if RS is perpendicular to OP , we have RS : OS : OR = PM : OM OP . Hence we conclude , that , disregarding signs , the values of the Trigonometrical Ratios are quite independent of the magni- tude of the revolving ... Page 9

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**revolving line**OP . It is from these relations , viz . that the cosine , cotangent , co- secant of an angle , are respectively the same as the sine , tangent , and secant of the complement , that they derive their names . From the ...### Other editions - View all

### Common terms and phrases

1+tan a+b+c a+B+y a+tan angle AOP AOP₁ arithmetical progression BERNARD DRAKE circular measure cloth complement Construct the angle cos² cosec cosine cot² cotangent Crown 8vo decimal distance equal equation Euclid EXAMPLES Fcap feet Fellow of St Fellow of Trinity Find the number foot formulæ given height horizontal plane hypothenuse inscribed circle John's College late Fellow loga logarithms M.A. Fellow magnitude miles negative angle number of degrees observes the angle opposite sides perpendicular polygon positive quadrant radii radius respectively revolving line right angle right-angled triangle sec² secant Second Edition Sermons sewed Shew sides and angles sin ß sin² sin² ß sin³ tan¹ tan² tan³ tangent tower Treatise Trigono Trigonometrical Ratios Trinity College unit of length University of Cambridge vers yards

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