## Elements of Plane Trigonometry |

### From inside the book

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**cosec**A , cot A. 1- cos A is defined to be the versed sine of A , or vers A. * - By the 47th Prop . of the 1st Book of Euclid , AP2 + DP2 = AD2 . It may be perhaps necessary to re- mark , that the following definitions have been given ... Page 8

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**cosec**A , cot A. 1. cos A is defined to be the versed sine of A , or vers A. * - By the 47th Prop . of the 1st Book of Euclid , AP2 + DP2 = AD2 ......... .. It may be perhaps necessary to re- r mark , that the following definitions have ... Page 9

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**cosec**A 12 or**cosec**A = 2 ' sin A sin A ( 6 ) versin Arcos A ( 7 ) AP AD cos A cot A cos A DP AD B 5 TRIGONOMETRY . 9 Divide both sides of this equation by AD2, and ... Page 10

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**cosec**A = - DP AD sin A sin A ' AD2 sec2 A AP2 + DP2 DP \ 2 = AP2 1+ - 1 + tan2 4 · AP2 or by dividing equation ( 1 ) by AP2 , ( 417 ) 2 + ( 22 ) 2 = ( 42 ) 2 ; or 1 + tan2 A sec2 A ; ... sec A = = √ ( 1 + tan2 4 ) . Also dividing ... Page 10

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**cosec**A = A ) , · △ ) .**cosec**After one revolution is completed , the sines , cosines , & c . , take the same values as before ; therefore the sine of any angle is the same as the sine of 360 ° + that angle , or sin A = sin ( 2π + ...### Other editions - View all

### Common terms and phrases

1+tan AB² AC² angle ACB AP AP AP AP² ARITHMETIC Asin Atan B+cot centre circular measure circumference cos² cos³ cosec cosine cot 4+cot cot A cot cot² OCA diameter distance equal equation Euclid feet Find the number formula given GRAMMAR height Hence hexagon inscribed circle IVY LANE J. R. Young King's College School log blog logarithms nth root number of degrees number of sides perimeter perpendicular plane triangle quadrant radii radius ratio regular polygon Rudimentary Treatise sec² shew sin A cos sin A sin sin¹ sin2 sin² 18 sin³ sine and cosine square subtend subtracted T. H. L. Leary tan-¹ tan² tangent triangle ABC Trigonometry unity VIRTUE BROTHERS W. D. Hamilton

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