Elementary Trigonometry |
From inside the book
Results 1-5 of 64
Page 5
... hence the ratio of A to B may be measured by the by B ; fraction A B In order to compare two quantities they must be expressed in terms of the same unit . Thus the ratio of 2 yards to 2 × 3 × 12 8 27 inches is measured by the fraction ...
... hence the ratio of A to B may be measured by the by B ; fraction A B In order to compare two quantities they must be expressed in terms of the same unit . Thus the ratio of 2 yards to 2 × 3 × 12 8 27 inches is measured by the fraction ...
Page 7
... hence from the definitions of Art . 11 it will be seen that those ratios which have the hypotenuse in the denominator can never be greater than unity , while those which have the hypotenuse in the numerator can never be less than unity ...
... hence from the definitions of Art . 11 it will be seen that those ratios which have the hypotenuse in the denominator can never be greater than unity , while those which have the hypotenuse in the numerator can never be less than unity ...
Page 10
... Hence the trigonometrical ratios may also be defined as trigonometrical functions ; for the present we shall chiefly em- ploy the term ratio , but in a later part of the subject the idea of ratio is gradually lost and the term function ...
... Hence the trigonometrical ratios may also be defined as trigonometrical functions ; for the present we shall chiefly em- ploy the term ratio , but in a later part of the subject the idea of ratio is gradually lost and the term function ...
Page 17
... hence the first side sec2 0 ( sec2 0 -1 ) = = ( 1 + tan2 0 ) tan2 0 = tan20 + tan1 0 . EXAMPLES . III . a . Prove the following identities : 1. sin A cot A = cos A. 2 . 3. cot A sec A = cosec A. 5. cos A cosec A = cot A. 7. ( 1 - cos2 A ) ...
... hence the first side sec2 0 ( sec2 0 -1 ) = = ( 1 + tan2 0 ) tan2 0 = tan20 + tan1 0 . EXAMPLES . III . a . Prove the following identities : 1. sin A cot A = cos A. 2 . 3. cot A sec A = cosec A. 5. cos A cosec A = cot A. 7. ( 1 - cos2 A ) ...
Page 22
... Hence cosec A = QR 12 ' and PQ 5 cot A = = QR 12 [ Compare Art . 32 , Ex . 2. ] Example 2. Find tan A and cos A in terms of cosec A. Take a triangle PQR right - angled at Q , and having △ RPQ = A . For shortness , denote cosec A by c ...
... Hence cosec A = QR 12 ' and PQ 5 cot A = = QR 12 [ Compare Art . 32 , Ex . 2. ] Example 2. Find tan A and cos A in terms of cosec A. Take a triangle PQR right - angled at Q , and having △ RPQ = A . For shortness , denote cosec A by c ...
Contents
164 | |
175 | |
184 | |
186 | |
193 | |
231 | |
273 | |
282 | |
49 | |
64 | |
65 | |
82 | |
106 | |
110 | |
119 | |
123 | |
127 | |
130 | |
138 | |
146 | |
152 | |
288 | |
296 | |
303 | |
309 | |
318 | |
326 | |
336 | |
2 | |
9 | |
13 | |
19 | |
37 | |
Other editions - View all
Common terms and phrases
1+cos 1+tan² a+cos A+tan acute angle angle of elevation B+cos centre circle College cos² cos³ cosec cosine cot² cyclic quadrilateral decimal denote diff equal equation ex-central triangle Example expression Fcap feet Find the angle find the distance find the height Find the number Find the value flagstaff following identities formula given log greatest angle Hence horizontal plane hypotenuse inscribed LAOB loga logarithm magnitude miles negative number of radians observer pedal triangle perpendicular polygon positive Prof Prove the following quadrant quadrilateral radian measure radius vector regular polygon right angle right-angled triangle sec² sexagesimal shew sides sin sin sin sin² sin³ sine solution solve the triangle subtends an angle supplementary angles tan² tangent tower triangle ABC trigono trigonometrical functions trigonometrical ratios π π
Popular passages
Page 10 - BLACKIE— GREEK AND ENGLISH DIALOGUES FOR USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACKIE, Professor of Greek in the University of Edinburgh.
Page 15 - TAYLOR— WORDS AND PLACES; or, Etymological Illustrations of History, Ethnology, and Geography. By the Rev. ISAAC TAYLOR, MA Third and cheaper Edition, revised and compressed. With Maps. Globe 8vo. 6s.
Page 24 - HO.W TO DRAW A STRAIGHT LINE: a Lecture on Linkages. By AB KEMPE. With Illustrations. Crown 8vo.
Page 25 - STABILITY OF A GIVEN STATE OF MOTION, PARTICULARLY STEADY MOTION. Adams
Page 6 - AN INTRODUCTION TO ARISTOTLE'S RHETORIC. With Analysis, Notes, and Appendices. By EM COPE, Fellow and Tutor of Trinity College, Cambridge. 8vo.
Page 12 - JOHNSON'S LIVES OF THE POETS. The Six Chief Lives (Milton, Dryden, Swift, A'ddison, Pope, Gray), with Macaulay's "Life of Johnson.
Page 21 - SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the Use of Schools. By JM WILSON, MA New Edition. Extra fcap. 8vo. 31. 6d. WILSON— GRADUATED EXERCISES IN PLANE TRIGONOMETRY.
Page 10 - MARSHALL — A TABLE OF IRREGULAR GREEK VERBS, classified according to the arrangement of Curtius
Page 10 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Page 34 - LOGIC. ELEMENTARY LESSONS IN LOGIC; Deductive and Inductive, with copious Questions and Examples, and a Vocabulary of Logical Terms. By W. STANLEY JEVONS, MA, Professor of Political Economy in University College, London. New Edition. Fcap. 8vo. 3*. 6d. " Nothing can be better for a school-book. "-^-GUARDIAN. "A manual alike simple, interesting, and scientific."— ATHHN/UJH.