A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of the Nature and Use of Logarithms. Being the Second Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges ...Howe & Deforest, 1815 - 126 من الصفحات |
من داخل الكتاب
النتائج 1-5 من 11
الصفحة 41
... cosecant of an angle is the secant of the complement of the angle . Thus CF is the cosecant of GCA . Hence , as in a right angled triangle , one of the acute an- gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent ...
... cosecant of an angle is the secant of the complement of the angle . Thus CF is the cosecant of GCA . Hence , as in a right angled triangle , one of the acute an- gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent ...
الصفحة 42
... cosecant . By comparing the triangles CBG and CAD , 1. AC : BC :: AD : BG , that is , R : cos :: tan : sin . 2. CG : CD :: BG : AD 3. CB : CA :: CG : CD R : sec : sin : tan . COS : R :: R : : sec . Therefore R2 = cos x sec . By ...
... cosecant . By comparing the triangles CBG and CAD , 1. AC : BC :: AD : BG , that is , R : cos :: tan : sin . 2. CG : CD :: BG : AD 3. CB : CA :: CG : CD R : sec : sin : tan . COS : R :: R : : sec . Therefore R2 = cos x sec . By ...
الصفحة 46
... cosecant of an angle , are the sine , tangent , and secant of the complement of the angle . ( Art . 69. ) As the complement of an angle is the difference between the angle and 90 ° , and as 45 is the half of 90 ; if any given angle ...
... cosecant of an angle , are the sine , tangent , and secant of the complement of the angle . ( Art . 69. ) As the complement of an angle is the difference between the angle and 90 ° , and as 45 is the half of 90 ; if any given angle ...
الصفحة 47
... cosecant of an angle greater than 45 ° , has its equal , among the sines , tangents , and secants of an- gles less than 45o , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to ...
... cosecant of an angle greater than 45 ° , has its equal , among the sines , tangents , and secants of an- gles less than 45o , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to ...
الصفحة 51
... cosecant . In fact , the secant is the arithmetical comple- ment of the cosine , with 10 added to the index . For the secant And the ar . comp . = 20 - cos of cos = 10 - cos ( Art . 54. ) So also the cosecant is the arithmetical ...
... cosecant . In fact , the secant is the arithmetical comple- ment of the cosine , with 10 added to the index . For the secant And the ar . comp . = 20 - cos of cos = 10 - cos ( Art . 54. ) So also the cosecant is the arithmetical ...
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
acute angle added angle ACB arithmetical complement arithmetical progression b+sin base calculation centre circle cosecant Cosine Cotangent Tangent decimal degrees and minutes divided division divisor equal to radius equation errour exponents extend find the angles find the logarithm fraction geometrical progression given angle given number given side Given the angle gles greater half the sum hypothenuse JEREMIAH DAY length less line of chords line of numbers lines of sines loga logarithmic sine logarithmic TANGENT metical Mult multiplied natural number natural sines number of degrees opposite angles perpendicular positive proportion quadrant quotient radix right angled triangle rithms root secant similar triangles sine of 30 sines and cosines slider square subtracting tables tabular radius tabular sine tangent of half theorem transverse distance triangle ABC trigonometrical tables Trigonometry versed sine vulgar fraction
مقاطع مشهورة
الصفحة 68 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
الصفحة 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
الصفحة 105 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
الصفحة 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
الصفحة 39 - With these the learner should make himself perfectly familiar. 82. The SINE of an arc is a straight line drawn from one end of the arc, perpendicular to a diameter which passes through the other end. Thus BG (Fig.
الصفحة 116 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
الصفحة 37 - The periphery of every circle, whether great or small, is supposed to be divided into 360 equal parts called degrees, each degree into 60 minutes, each minute into 60 seconds, each second into 60 thirds, &c., marked with the characters °, ', ", '", &c. Thus, 32° 24...
الصفحة 72 - ... angle. The third angle is found by subtracting the sum of the other two from 180° ; and the third side is found as in Case I.