## Academic Trigonometry: Plane and Spherical |

### From inside the book

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**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 - sin B tan ( 4 - B ) SPHERICAL ... Page 26

Plane

Plane

**and**Spherical Thomas Marcus Blakslee. FUNCTIONS OF**HALF**ANGLES . Plane . By law of cosines ,**cos A**= a2 − ( b2 + c2 ) b2 + c2 — a2 - = - - 2 bc 2 bc PROBLEM . To substitute this value in**1**±**cos A**,**and**thus find the functions of the ... Page 27

... tan = 2 S- a • S cos A = FORMULAS FOR HALF ANGLES . Spherical . By law of cosines , cos a cos b cos c - sin b sin ... one - half of either angle of a spheri- cal triangle is equal to the square root of the

... tan = 2 S- a • S cos A = FORMULAS FOR HALF ANGLES . Spherical . By law of cosines , cos a cos b cos c - sin b sin ... one - half of either angle of a spheri- cal triangle is equal to the square root of the

**sine of one - half**of the ... Page 30

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**tangent of one - half**the sum of the angles opposite . THEOREM 3. The**sine of one - half**the sum of either two angles of any spherical triangle is to the**sine of one - half**their differ- ence as the**tangent of one - half**the side which ...### 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 cos² 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 sin² 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...