A Treatise on Plane and Spherical Trigonometry |
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applied B+AB becomes C+AC C₁ coefficients computation constant cos A cos cos A sin cos² cos³ cosb cosc cosec cosm Csin deduce denote differential employed equal equations EXAMPLE expressed factors formulæ gives imaginary increments integer less than 180 log cot logarithms multiple angle negative obtain opposite perp perpendicular plane triangle polar triangle positive preceding article quadrant radius reduced right angle right triangles second member sides simple angle sin b cos sin b sin sin x sin² sin³ sine sine and cosine solution solve the triangle spherical triangle spherical trigonometry Substituting the values tables tan-¹ tan² tan³ tangent theorem Trig trigonometric functions whence 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 169 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
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 16 - The sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity.
Page 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90°.
Page 238 - 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 179 - ... the sign of cos A, is the same as that of cos a, that is, A and a are in the same quadrant.
Page 65 - The side opposite the given angle is to the side opposite the required angle as the sine of the given angle is to the Bine of the required angle.
Page 169 - ... the cosine of the hypotenuse is equal to the product of the cosines of the two sides.