The Elements of Plane and Spherical Trigonometry |
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Page 9
... perpendicular to the diameter passing through the beginning of it . ( 2 ) The Tangent of an arc BP is the straight line BT touching the arc at the beginning , and terminated by the radius , through the end of it , produced . ( 3 ) The ...
... perpendicular to the diameter passing through the beginning of it . ( 2 ) The Tangent of an arc BP is the straight line BT touching the arc at the beginning , and terminated by the radius , through the end of it , produced . ( 3 ) The ...
Page 11
... perpendicular to AC ; then , we have the following Definitions . B A C BC ( 1 ) Sin A = = or BC AB sin A : AB ' AC ( 2 ) Cos A = = or AC AB cos A : AB ' ( 3 ) Tan A = BC AC ' = or BC AC tan A : ( 4 ) AC Cot A = BC ' = or AC BC cot A ...
... perpendicular to AC ; then , we have the following Definitions . B A C BC ( 1 ) Sin A = = or BC AB sin A : AB ' AC ( 2 ) Cos A = = or AC AB cos A : AB ' ( 3 ) Tan A = BC AC ' = or BC AC tan A : ( 4 ) AC Cot A = BC ' = or AC BC cot A ...
Page 20
... perpendicular to BD , and this will bisect both the angle BAD and the side BD : then △ BAD = } of two right angles = 60 ° , and .. BAC = 30 ° : whence we have sin 30 ° : = BC BD AB 1 AB AB AB = = = == cos 60 ° : - .. cos 30 ° = √1 ...
... perpendicular to BD , and this will bisect both the angle BAD and the side BD : then △ BAD = } of two right angles = 60 ° , and .. BAC = 30 ° : whence we have sin 30 ° : = BC BD AB 1 AB AB AB = = = == cos 60 ° : - .. cos 30 ° = √1 ...
Page 25
... perpendicular to OQ ; DF , EG perpendicular to OP ; and EH parallel to OP , meeting FD in H : then , AEOG = - HEO = 900 – L DEH : .. sin A = cos DEH = EH ED ' HD = and cos A sin DEH : = ED ' by the definitions of Article ( 24 ) ; whence ...
... perpendicular to OQ ; DF , EG perpendicular to OP ; and EH parallel to OP , meeting FD in H : then , AEOG = - HEO = 900 – L DEH : .. sin A = cos DEH = EH ED ' HD = and cos A sin DEH : = ED ' by the definitions of Article ( 24 ) ; whence ...
Page 26
... perpendicular to OP ; and EH parallel to OP meeting FD produced in H : a Ꭱ E H G F Р then , AEOG : = △ HEQ = 90o – △ DEH : - .. sin A = cos DEH : EH HD = and cos Asin DEH = ED ED by the definitions of ( 24 ) ; whence , as before , GE ...
... perpendicular to OP ; and EH parallel to OP meeting FD produced in H : a Ꭱ E H G F Р then , AEOG : = △ HEQ = 90o – △ DEH : - .. sin A = cos DEH : EH HD = and cos Asin DEH = ED ED by the definitions of ( 24 ) ; whence , as before , GE ...
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
algebraical angular appears applied arithmetical Article assuming base called Cambridge centre chapter circle circular circumscribed cloth College contained corresponding cos a cos cos² cosec determined distance drawn easily Edition equal equation evidently expressed factors figures follows formulę functions given gives greater Hence imaginary immediately inscribed latter less lines logarithms magnitude means measure meet nearly negative object observed obtained opposite perpendicular places plane polygon positive practical produced prove quadrant quantity radius regular respectively rest right angles roots sides signs similarly sin a sin sin² sin³ sine and cosine solution sphere spherical triangle square surface tables Theorem Trigonometry values vers whence
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