Elementary Trigonometry |
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Page 32
... sine QP of the angle EQP , QM ( 2 ) cosine QP PM ( 3 ) tangent QM ( 4 ) ( 3 ) ( 2 ) ( 1 ) P Q M Р QP ( 4 ) PM W M Q W E E EW M Q E M P cosecant QP ( 5 ) secant QM QM ( 6 ) cotangent PM 52 . It will be observed that cosecant EQP = = 1 sine ...
... sine QP of the angle EQP , QM ( 2 ) cosine QP PM ( 3 ) tangent QM ( 4 ) ( 3 ) ( 2 ) ( 1 ) P Q M Р QP ( 4 ) PM W M Q W E E EW M Q E M P cosecant QP ( 5 ) secant QM QM ( 6 ) cotangent PM 52 . It will be observed that cosecant EQP = = 1 sine ...
Page 33
... sine , thus , versed sine EQP = 1 - cos EQP . 54. Care must be taken in representing these ratios alge- braically to put the complete algebraic representative for each line . Thus let EQW be the primitive line and a diameter of a circle ...
... sine , thus , versed sine EQP = 1 - cos EQP . 54. Care must be taken in representing these ratios alge- braically to put the complete algebraic representative for each line . Thus let EQW be the primitive line and a diameter of a circle ...
Page 34
... sine and the cosine . Referring to the diagrams of Art . 51 , PM sine EQP = QP ' cosine EQP = QM = QP ' In each case the denominator of the fraction is formed by that side of the triangle of reference which is opposite to the right ...
... sine and the cosine . Referring to the diagrams of Art . 51 , PM sine EQP = QP ' cosine EQP = QM = QP ' In each case the denominator of the fraction is formed by that side of the triangle of reference which is opposite to the right ...
Page 35
... sine of a given angle we must take as the numerator of the fraction that side of our triangle of reference which is opposite to the given angle ; and in determining the ratio which we call the cosine of a given angle we must take as the ...
... sine of a given angle we must take as the numerator of the fraction that side of our triangle of reference which is opposite to the given angle ; and in determining the ratio which we call the cosine of a given angle we must take as the ...
Page 36
... sine and the cosine , he will be able to determine the other four ratios without any trouble . EXAMPLES . - XIII . ( 1 ) Let ABC be a triangle . Draw from B a perpendicular BD on AC , and let it be within the triangle . Then write the ...
... sine and the cosine , he will be able to determine the other four ratios without any trouble . EXAMPLES . - XIII . ( 1 ) Let ABC be a triangle . Draw from B a perpendicular BD on AC , and let it be within the triangle . Then write the ...
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Common terms and phrases
angle AOP angle be expressed angle EQP angle whose circular Arithmetical Progression Cambridge centre circle circular measure circumference College List convert the measure cos² cos³ cosec cosine Crown 8vo Edition equal expressed in degrees feet find the angle find the number following angles formula given angle contain Given find Given log Greek Isocrates John Edwin Sandys John Henry Blunt Let the given logarithm magnitude minutes and seconds multiply the measure negative number of degrees number of grades Pall Mall QP revolves radius regular polygon right angles right-angled triangle School and College Sexagesimal shew sides sin² sin³ sine subtends an angle tan² tan³ tangent Thomas Kerchever Arnold Thucydides triangle ABC Trigonometrical Ratios Trinity College unit of angular unit of circular Waterloo Place π π
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