## A Treatise on Plane and Spherical Trigonometry |

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according angle applied approximate becomes CHAPTER Check circle computation considered constant corresponding cos a cos cos x cosc cosec deduce denote determined develop difference differential divided easily employed equal equations EXAMPLE expressed factors formulæ functions given gives greater half imaginary increments less than 180 log cot logarithms manner means method middle multiple nearly necessary negative observing obtain opposite perpendicular plane triangle positive preceding problem quadrant quantities radius reduced relations right angle right triangles roots Rules second member shown sides similar simple sin A sin sin c cos sin x sine sine and cosine sinº solution solve sphere spherical triangle Substituting successively tables taken tangent third Trig trigonometric unity values whence

### 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 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 58 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90°.

Page 34 - I sin y \2 / \2 / = sin x cos y + cos x sin y, sin (a; — y) = sin (x + (— y)) = sin a; cos (— y) + cos a; sin (— y) = sin x cos y — cos x sin y, tan (x + y) = sin (x + y) sin x cos y + cos x...

Page 64 - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.

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 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 150 - 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 244 - If the sides of a triangle are very small compared with the radius of the sphere and a plane triangle be formed whose sides are equal to those of the spherical triangle...