## Elements of Plane and Spherical Trigonometry: With Practical Applications |

### From inside the book

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Page 14

... of sine , tangent ,

... of sine , tangent ,

**secant**, cosine , cotangent , and cosecant . There are also sometimes employed the quantities termed versed sine , coversed sine , and suversed sine . 47. The SINE of an angle is the ratio of 14 TRIGONOMETRY . Page 15

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**SECANT**of an angle is the ratio of the hypothenuse to the adjacent side . h h Thus , sec A = sec B p ( 3 ) 50. The COSINE , COTANGENT , and COSECANT of an angle are respectively the SINE , TANGENT , and**SECANT**of its complement . Hence ... Page 16

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**secant**, & c . , were formerly * sidered to be functions of an arc , and denoted certain trigonome- tric lines . Α ' Cot . T ' T D'e CARB Sec Thus , let O be the centre of any circle , AA " its diameter , and AB any arc ; draw the ... Page 17

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**secant**, O T ' its cosecant , AD its versed sine , A ' D ' its coversed sine , and A " D its suversed sine . is the chord of the arc A B. Also the line joining A and B That is , in the circle whose radius is unity ; - The SINE of an arc ... Page 19

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**SECANT**and COSECANT of an angle by means of the tangent . From the right - angled triangle ABC B we have h2 = b2 + p2 . Dividing both sides of the equation by b2 , gives p3 ba = 1 + or , by definitions ( Art . 48 , 49 ) , A C sec2 A = 1 ...### Other editions - View all

### Common terms and phrases

A B C A+ log acute angle adjacent sides Algebra angle equal angle of elevation angle opposite angle or arc ar.co.log Arithme column headed cos² cosec Cotang decimal denoted divided Elementary Algebra equation Equations Art EXAMPLES feet find the SINE formulæ Geom Geometry given number Given the hypothenuse Greenleaf's New Series half the sum Hence included angle log cos log cot log sin logarithmic cosine logarithmic sine logarithmic tangent M.
M. Sine minus the logarithmic Napier's rules negative oblique oblique-angled spherical triangle Parker's Exercises perpendicular plane triangle Prop right-angled spherical triangle right-angled triangle equal rods School secant side b equal side opposite sin A cos sin A sin sin a+b sin² sine and cosine Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers suversed sine Tang tangent of half trigonometric functions values whence yards

### Popular passages

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 7 - This process, like its converse (Art. 23), is based upon the supposition that the differences of logarithms are proportional to the differences of their corresponding numbers.

Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.

Page 74 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...

Page 43 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Page 39 - ... be at the head of the column, take the degrees at the top of the table, and the minutes on the left ; but if the name be at the foot of the column, take the degrees at the bottom, and the minutes on the right.

Page 46 - The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.