A Treatise on Plane and Spherical Trigonometry |
Common terms and phrases
a₁ applied becomes C+AC C₁ coefficients computation constant cos A cos cos B sin cos² cos³ cosb cosc cosec cosm deduce denote difference differential employed equal equations EXAMPLE expressed factors formulæ gives hypotenuse imaginary increments integer less than 90 log cot logarithms multiple angle Napier's Rules negative obtain perpendicular plane triangle polar triangle positive preceding article quadrant quotient radius reduced right angle right triangles second member simple angle sin b sin sin c cos sin x sin² sin³ sine sine and cosine solution solve the triangle spherical triangle spherical trigonometry Substituting the values t₁ tables tan-¹ tan² tan³ tangent theorem Trig trigonometric functions whence x₁ zero Δα
Popular passages
Page 151 - 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...
Page 152 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 181 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 2 - Union, in the Clerk's Office of the District Court of the Eastern District of Pennsylvania. PREFACE.
Page 244 - A, 4 cos 6 = cos c cos a + sin c sin a cos B, > (1) . , "cos c = cos a cos b + sin a sin b cos C. J Whence . cos a — cos b...
Page 58 - THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 229 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 215 - The demonstration is very simple ; in fact we have sin b sin c + cos b cos c cos A = sin b sin c (sina A + cos'2 A) + cos b cos c cos A = sin b sin c sin2 A + cos A (cos b...
Page 169 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90°.