## Academic Trigonometry: Plane and Spherical |

### From inside the book

Results 1-5 of 8

Page 20

... angles , page 14 , sin ( A — B ) = sin A cos B - cos A sin B. cos ( A - B ) = cos A cos B + sin A sin B. tan Atan B ( 1 ) ( 2 ) tan ( A - B ) = ( 3 ) 1 + tan Atan B ( b )

... angles , page 14 , sin ( A — B ) = sin A cos B - cos A sin B. cos ( A - B ) = cos A cos B + sin A sin B. tan Atan B ( 1 ) ( 2 ) tan ( A - B ) = ( 3 ) 1 + tan Atan B ( b )

**Half Angle**. By double angle formulas , A cos2 + sin2 = 1 . A 2 2 ... Page 22

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**angles**.**Half**sum = greater**half**difference . - sin A + sin B = 2 YY ' = 2 sin VY ' . 2 5. ( cos Acos B ) 2 + ( sin A − sin B ) 2 = 4 sin2 : - 6. cos 2 A = ( 1 — tan2A ) : ( 1 + tan2A ) . A B 2 180 ° 7. As 2π = 360 ° , 2 ° = = 57.3 . π ... Page 24

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**angle**is to their difference as the tangent of one -**half**the sum of the opposite**angles**is to the tangent of one -**half**their difference . By law of sines and theory of proportion , a + bsin A + sin B a = 1⁄2 tan ( A + B ) . b sin A ... Page 25

... b cos A. Substituting and transposing factor cos b , cosa cosb cos c + sin b sin c cos A. For Analogy of Law of Tangents , see the limit of Napier's ( 2 ) , page 29 . FUNCTIONS OF

... b cos A. Substituting and transposing factor cos b , cosa cosb cos c + sin b sin c cos A. For Analogy of Law of Tangents , see the limit of Napier's ( 2 ) , page 29 . FUNCTIONS OF

**HALF ANGLES**. Plane . By law of LAWS . 25. Page 26

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**half angles**in terms of the sides . If a + b + c = 28 , .. a + b - c = 2 ( sc ) , a - b + c = 2 ( 8 - b ) , b + c ... half an angle of a plane triangle is equal to the square root of half the sum of the three sides minus one of the ...### Other editions - View all

### Common terms and phrases

35 cents 40 cents 80 Lotze's Outlines acute angle Algebra analogy Analytic Geometry Arithmetic BOSTON Calculus circle Cloth Copies sent cos(a cosē cosine of one-half cot H distance ecliptic Equations Examination Manual Exercise Manual functions GAUSS EQUATIONS GINN & COMPANY Greek HALF ANGLES Half morocco hypotenuse Introduction Price Lafayette College Latin Grammar law of cosines law of sines Law of Tangents Lexicon Logarithms Mailing Price Mathe matics morocco Napier's one-half the sum one-half their difference Plane and Spherical Plane Trigonometry problems Prof Professor of Mathematics Pythagorean QUADRANTAL TRIANGLES radius receipt of Introduction Right ascension right triangles sent to Teachers Shakespeare sin b sin sin(s sinē sine and cosine sine of one-half Solid Geometry spherical triangle Spherical Trigonometry Surveying Syllabus T. M. BLAKSLEE Tables tangent of one-half Teachers for Examination THEOREM Trig view to Introduction Wentworth & Hill's

### Popular passages

Page 25 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...

Page 25 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...