Elements of Plane and Spherical Trigonometry |
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Page vi
... regarded as per- forming a trifling service to the English student . I am aware that there are some persons , into whose hands this work may fall , who will not approve it as they would have done had the demonstrations been exclu ...
... regarded as per- forming a trifling service to the English student . I am aware that there are some persons , into whose hands this work may fall , who will not approve it as they would have done had the demonstrations been exclu ...
Page 8
... regarded as the radius of the 2. tan√ ( sec2 - 1 ) . 4. cosec √ ( 1 + cot2 ) . sin 1 5. tan = 6. cot COS COS sin 7. sec 8. cosec = COS sin . 20. From these and other properties and theorems , some of which will be demonstrated as we ...
... regarded as the radius of the 2. tan√ ( sec2 - 1 ) . 4. cosec √ ( 1 + cot2 ) . sin 1 5. tan = 6. cot COS COS sin 7. sec 8. cosec = COS sin . 20. From these and other properties and theorems , some of which will be demonstrated as we ...
Page 22
... regarded as the sine of 1 ' ; and in fact the sine given in the tables which run to seven places of figures is ' 0002909. By chap . i . art . 19 , we have , for any arc , cos = √ ( 1 − sin2 ) . This theorem gives , in the pre- sent ...
... regarded as the sine of 1 ' ; and in fact the sine given in the tables which run to seven places of figures is ' 0002909. By chap . i . art . 19 , we have , for any arc , cos = √ ( 1 − sin2 ) . This theorem gives , in the pre- sent ...
Page 37
... ' , the sine diminishes , but is to be regarded as positive till the arc becomes AEA ' er 180 ° . In that state of the arc the value of the sine is obviously 0. Passing on to the third quadrant , Analytical Plane Trigonometry . 37.
... ' , the sine diminishes , but is to be regarded as positive till the arc becomes AEA ' er 180 ° . In that state of the arc the value of the sine is obviously 0. Passing on to the third quadrant , Analytical Plane Trigonometry . 37.
Page 38
... regarded as negative . In this state it continues to increase through the third quadrant , at the end E ' of which it is again equal to radius . From thence the ne- gative value of the sine diminishes , till at the end A of the fourth ...
... regarded as negative . In this state it continues to increase through the third quadrant , at the end E ' of which it is again equal to radius . From thence the ne- gative value of the sine diminishes , till at the end A of the fourth ...
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Common terms and phrases
altitude angled spherical triangle axis azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius rectangle right angled spherical right angled triangle right ascension right line secant sin a sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence yards zenith
Popular passages
Page 4 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 248 - SCIENTIFIC DIALOGUES ; intended for the Instruction and Entertainment of Young People ; in which the first principles of Natural and Experimental Philosophy are fully explained, by the Rev.
Page 225 - ... third of the excess of the sum of its three angles above two right angles...
Page 19 - In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides.
Page 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 249 - OSTELL'S NEW GENERAL ATLAS; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Page 34 - Call any one of the sides radius, and write upon it the word radius ; observe whether the other sides become sines, tangents, or secants, and write those words upon them accordingly. Call the word written upon each side the name of each side ; then say, As the name of the given side, Is to the given side ; So is the name of the required side, To the required side.
Page 69 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 18 - AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 83 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...