## 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 ... |

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**equal**to 90o . The angles ACB and DCB are together**equal**to a right angle . The two acute angles of a right an- gled ...**radius**of the**circle**. In many calculations , it is convenient to consider the**radius**, whatever be its length ... Page 41

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**equal**CB , is the sine of HCG . ( Art . 82. ) It is , therefore , the cosine of GCA . On the other hand GB is the ...**radius**. But the versed sine of an obtuse angle is**equal**to the sum of the co- sine and**radius**. Thus the versed ... Page 42

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**equal**; ( Euc . 29. 1. ) as are also the angles GCB , LGC , and HFC . The triangles ACD , BCG , and HCF are ...**radius**, sin for sine , tan for tangent , sec for secant , cos for cosine , cot for cotangent , cosec for cosecant . By ... Page 43

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**equal**to the And the tangent of 45 ° S**radius**, and therefore**equal**to each other . Demonstration . 1. In the quadrant ACH , ( Fig . 5. ) the arc AH is 90o . The sine of this , according to the definition , ( Art . 82. ) is CH , the**radius**... Page 44

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**equal to radius**. Its half , therefore , which is the sine of 30 ° is equal to half radius . Cor . The cosine of 60 ° is equal to half radius . For the cosine of 60 ° is the sine of 30 ° . ( Art . 89. ) . 97. The chord of any arc is a ...### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 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.

Page 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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...

Page 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.