Trigonometry for Beginners with Numerous ExamplesMacmillan, 1868 - 200 σελίδες |
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Σελίδα 9
... , = X = = 1 , 1 1 therefore cosec A = sin A = sin A ' cosec A ' PM Also PM AM sin A tan A = == = AM AP AP cos A ; AM cot A = PM - АМ PM AP АР cos A = = sin A ' 20. To shew that ( sin A ) + ( TRIGONOMETRICAL RATIOS . 9.
... , = X = = 1 , 1 1 therefore cosec A = sin A = sin A ' cosec A ' PM Also PM AM sin A tan A = == = AM AP AP cos A ; AM cot A = PM - АМ PM AP АР cos A = = sin A ' 20. To shew that ( sin A ) + ( TRIGONOMETRICAL RATIOS . 9.
Σελίδα 10
Isaac Todhunter. 20. To shew that ( sin A ) + ( cos A ) = 1 . A M B In the right - angled triangle APM we have PM2 + AM2 = AP2 ; PM2 + AM2 therefore = AP2 = 1 , therefore PM2 AM ? + AP2 ... shew that ( sec A ) 2 10 TRIGONOMETRICAL RATIOS .
Isaac Todhunter. 20. To shew that ( sin A ) + ( cos A ) = 1 . A M B In the right - angled triangle APM we have PM2 + AM2 = AP2 ; PM2 + AM2 therefore = AP2 = 1 , therefore PM2 AM ? + AP2 ... shew that ( sec A ) 2 10 TRIGONOMETRICAL RATIOS .
Σελίδα 11
Isaac Todhunter. 23 . To shew that ( sec A ) 2 = 1 + ( tan A ) 2 , and ( coscc A ) 2 = 1 + ( cot A ) 2 . In the right - angled triangle APM ( see fig . to Art . 20 ) AP2 = AM2 + PM2 , we have AP2 PM2 therefore 1+ AM2 AM 29 therefore = 1 ...
Isaac Todhunter. 23 . To shew that ( sec A ) 2 = 1 + ( tan A ) 2 , and ( coscc A ) 2 = 1 + ( cot A ) 2 . In the right - angled triangle APM ( see fig . to Art . 20 ) AP2 = AM2 + PM2 , we have AP2 PM2 therefore 1+ AM2 AM 29 therefore = 1 ...
Σελίδα 29
... Shew that the tangents of 60 ° , 45 ° , and 15o are in Arithmetical Progression . 9. At a distance of 100 feet from the foot of a tower the tower subtends an angle of 30 ° ; find the height of the tower . 10. A base AB of 100 yards is ...
... Shew that the tangents of 60 ° , 45 ° , and 15o are in Arithmetical Progression . 9. At a distance of 100 feet from the foot of a tower the tower subtends an angle of 30 ° ; find the height of the tower . 10. A base AB of 100 yards is ...
Σελίδα 33
... shew in the next three Articles what are the chief advantages of the common system of logarithms . 59. In the common system of logarithms if the loga- rithm of any number be known , we can immediately deter- mine the logarithm of the ...
... shew in the next three Articles what are the chief advantages of the common system of logarithms . 59. In the common system of logarithms if the loga- rithm of any number be known , we can immediately deter- mine the logarithm of the ...
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Trigonometry for Beginners, with Numerous Examples Isaac Todhunter Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2010 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A-sin A+B+C Algebra angle increases angle PAB angles in terms angles included AP coincides AP moves Arithmetical Arithmetical Progression B-cos Cambridge centre circle circular measure circumference cloth cos² cos³ cosec cosine cotangent Crown 8vo decreases numerically determine distance draw PM perpendicular ELEMENTARY Euclid example expression Fcap feet figure find log find the height formulæ four right angles given angle Given log Hence hypotenuse increases from 180 inverse notation L sin logarithm Mathematical multiple of four negative and decreases number of degrees observe the angle opposite side plane positive angle preceding Article present Chapter quadrant PM regular polygon right-angled triangle sec² secant Second Edition shew sin A sin sin A+ sin sin sin sin² sin³ sine student suppose Tables tangent TREATISE Trigono Trigonometrical Ratios vers yards zero ОР
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