The Elements of Plane and Spherical Trigonometry |
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Page 8
... signs + and - , are necessarily supposed to be of the same kind . 19. We have now seen how an angle may be mea- sured by means of the radius of a circle whose centre is the angular point , and the arc which subtends it and we shall next ...
... signs + and - , are necessarily supposed to be of the same kind . 19. We have now seen how an angle may be mea- sured by means of the radius of a circle whose centre is the angular point , and the arc which subtends it and we shall next ...
Page 15
... Signs and , according to a principle which we shall now proceed to explain . Let DAB be a straight line , along ... signs of sin ( 90 ° + A ) and cosec ( 90 ° + A ) are + , whilst those of the other functions are Simi- larly , the signs ...
... Signs and , according to a principle which we shall now proceed to explain . Let DAB be a straight line , along ... signs of sin ( 90 ° + A ) and cosec ( 90 ° + A ) are + , whilst those of the other functions are Simi- larly , the signs ...
Page 16
... signs are easily derived from the equalities , sec α = дов COS a and cosec a = · до 2 sin a and are therefore identical with those of the cosine and sine respectively . Also , chord a = 2 sina is positive , since a is always terminated ...
... signs are easily derived from the equalities , sec α = дов COS a and cosec a = · до 2 sin a and are therefore identical with those of the cosine and sine respectively . Also , chord a = 2 sina is positive , since a is always terminated ...
Page 17
... signs of the corresponding functions : and though it be desirable that they should all be committed to memory , those of most frequent occurrence are here repeated : Sin 00 : Cos 0 ° - : 1 : Tan 0 ° = 0 : sin 90o 1 : sin 180 ° = 0 ...
... signs of the corresponding functions : and though it be desirable that they should all be committed to memory , those of most frequent occurrence are here repeated : Sin 00 : Cos 0 ° - : 1 : Tan 0 ° = 0 : sin 90o 1 : sin 180 ° = 0 ...
Page 18
... Signs : thus , cot ( -4 ) = - cot A : sec ( -4 ) = sec A : cosec ( -A ) = - cosec A : vers ( -4 ) = 1 − cos A : covers ( -A ) = 1 + sin A. - Hence , the ratios for A and A are equal in magni- tude , but different in algebraical sign ...
... Signs : thus , cot ( -4 ) = - cot A : sec ( -4 ) = sec A : cosec ( -A ) = - cosec A : vers ( -4 ) = 1 − cos A : covers ( -A ) = 1 + sin A. - Hence , the ratios for A and A are equal in magni- tude , but different in algebraical sign ...
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Other editions - View all
The Elements of Plane and Spherical Trigonometry: Designed for the Use of ... John Hind No preview available - 2012 |
The Elements of Plane and Spherical Trigonometry: Designed for the Use of ... John Hind No preview available - 2018 |
Common terms and phrases
a+b+c angular points arithmetical Article bisecting Cambridge centre circular measure circumscribed circle College corresponding cos a cos cos² cos³ cosec cosine Demoivre's Theorem denote Diff Edition equal equation express the sine find the rest formulæ functions Geometry given greater Hence imaginary inscribed John Machin logarithms magnitude multiple nearly negative number of sides number of terms obtained perpendicular places of decimals plane prove quadrant quadratic factors quantities r₁ radii radius regular polygon respectively right angles roots sec² shew sin A cos sin A sin sin² sin³ sin³A sine and cosine solid angle solution spherical triangle straight line tan-¹ tan'a tan² tan³ tangent triangle ABC Trigonometry values vers whence
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