Elementary Trigonometry |
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Page 53
... formulæ hold good for all magni- tudes of the angle which we have represented by the letter A , that is , not only but also ánd and and and sin3 A + cos3 A = 1 , sin0 + cos2 0 = 1 , sin x + cos x = 1 , sin 45 ° + cos2 45o = 1 , sin 60 ...
... formulæ hold good for all magni- tudes of the angle which we have represented by the letter A , that is , not only but also ánd and and and sin3 A + cos3 A = 1 , sin0 + cos2 0 = 1 , sin x + cos x = 1 , sin 45 ° + cos2 45o = 1 , sin 60 ...
Page 79
... formulæ ob- tained from Art . 100 . Ex . sin ( -825 ° ) sin ( 1080 ° -825 ° ) = sin 255 ° - sin 75 ° , = tan ( -135 ° ) = - tan 135 ° == tan 45o . EXAMPLES . - XXV . Find the values of the following ratios : ( 1 ) sin 480 . ( 2 ) cos ...
... formulæ ob- tained from Art . 100 . Ex . sin ( -825 ° ) sin ( 1080 ° -825 ° ) = sin 255 ° - sin 75 ° , = tan ( -135 ° ) = - tan 135 ° == tan 45o . EXAMPLES . - XXV . Find the values of the following ratios : ( 1 ) sin 480 . ( 2 ) cos ...
Page 81
... formulæ : sin ( A + B ) = sin A. cos B + cos A. sin B , cos ( A + B ) = cos A. cos B - sin A. sin B , sin ( A – B ) = sin A. cos B - cos A. sin B , cos ( AB ) = cos A. cos B + sin A. sin B ; by means of which we can express the sine and ...
... formulæ : sin ( A + B ) = sin A. cos B + cos A. sin B , cos ( A + B ) = cos A. cos B - sin A. sin B , sin ( A – B ) = sin A. cos B - cos A. sin B , cos ( AB ) = cos A. cos B + sin A. sin B ; by means of which we can express the sine and ...
Page 86
... formulæ established in this chapter to prove the following relations between the Trigonometrical Functions of angles . ( 2 ) sin ( 180 ° + A ) = − sin A. ( 1 ) cos ( 90 ° + 4 ) = — sin 4 . ( 3 ) cos ( π + 0 ) = cos 0 . ( 4 ) sin 3п + 0 ...
... formulæ established in this chapter to prove the following relations between the Trigonometrical Functions of angles . ( 2 ) sin ( 180 ° + A ) = − sin A. ( 1 ) cos ( 90 ° + 4 ) = — sin 4 . ( 3 ) cos ( π + 0 ) = cos 0 . ( 4 ) sin 3п + 0 ...
Page 87
... formulæ of Arts . 113 , 114 , we next arrange them thus : sin ( A + B ) = sin A. cos B + cos A. sin B , - sin ( A – B ) = sin A. cos B - cos A. sin B , cos ( A – B ) ... formulæ may be put in this form TRIGONOMETRICAL RATIOS OF TWO ANGLES . 87.
... formulæ of Arts . 113 , 114 , we next arrange them thus : sin ( A + B ) = sin A. cos B + cos A. sin B , - sin ( A – B ) = sin A. cos B - cos A. sin B , cos ( A – B ) ... formulæ may be put in this form TRIGONOMETRICAL RATIOS OF TWO ANGLES . 87.
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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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