# A Treatise on Plane and Spherical Trigonometry

H. Perkins, 1852
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### Contents

 PART I 9 CHAPTER III 22 CHAPTER V 43 SOLUTION OF PLANE RIGHT TRIANGLES 51 Additional Formula for Right Triangles 57 SOLUTION OF PLANE OBLIQUE TRIANGLES 64 CHAPTER IX 75 CHAPTER X 85
 TRIGONOMETRIC SERIES CONTINUED MULTIPLE ANGLES 135 SPHERICAL TRIGONOMETRY 149 GENERAL FORMULĘ 161 SOLUTION OF SPHERICAL RIGHT TRIANGLES 167 CHAPTER IV 177 127 183 141 189 AREA OF A SPHERICAL TRIANGLE 229

 CHAPTER XIII 115
 CHAPTER VII 241

### 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...