The Elements of Plane and Spherical Trigonometry |
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Page 10
... evidently remain the same . 21. COR . Since Pm in the latter diagram is equal to AM in the former , the cosine of an arc BP is equal to the straight line AM intercepted between the centre and the sine , and may be defined accordingly ...
... evidently remain the same . 21. COR . Since Pm in the latter diagram is equal to AM in the former , the cosine of an arc BP is equal to the straight line AM intercepted between the centre and the sine , and may be defined accordingly ...
Page 15
... evidently a posi- tive quantity : but if M be situated in AD , then MB is greater than AB , and the corresponding value of AM becomes negative , and we have AM = MB - AB = - ( AB – MB ) : whence , if lines measured from the fixed point ...
... evidently a posi- tive quantity : but if M be situated in AD , then MB is greater than AB , and the corresponding value of AM becomes negative , and we have AM = MB - AB = - ( AB – MB ) : whence , if lines measured from the fixed point ...
Page 29
... evidently enable us to express , in the forms of Sums or Differences , each of the Products in their latter members , and they deserve attention . Ex . If A = 30 ° , we shall have - sin ( 30o + B ) + sin ( 30 ° – B ) = 2 sin 30o cos B ...
... evidently enable us to express , in the forms of Sums or Differences , each of the Products in their latter members , and they deserve attention . Ex . If A = 30 ° , we shall have - sin ( 30o + B ) + sin ( 30 ° – B ) = 2 sin 30o cos B ...
Page 32
... evidently be used according as cos A is greater or less than sin A , ór , according as A is less or greater than 45o , by example ( 1 ) of Article ( 35 ) : ..cos A = { √√1 + sin 24 ± √√1 32 SINES AND COSINES OF The Sine and Cosine ...
... evidently be used according as cos A is greater or less than sin A , ór , according as A is less or greater than 45o , by example ( 1 ) of Article ( 35 ) : ..cos A = { √√1 + sin 24 ± √√1 32 SINES AND COSINES OF The Sine and Cosine ...
Page 46
... evidently be continued for angles of all magnitudes , if it be found necessary . ( 3 ) To find the sines and cosines of angles from 1 ° to 30 ° , The formula which may be used are , ( sin 46 THE TRIGONOMETRICAL CANON .
... evidently be continued for angles of all magnitudes , if it be found necessary . ( 3 ) To find the sines and cosines of angles from 1 ° to 30 ° , The formula which may be used are , ( sin 46 THE TRIGONOMETRICAL CANON .
Contents
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63 | |
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163 | |
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338 | |
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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