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

### From inside the book

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Page 33

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**tangent of half**the sum of the angles is to the**tangent of half**their difference , or as the cotangent of half their difference is to the co-**tangent of half**their sum . 89. By means of ( 62 ) , ( 63 ) , ( 64 ) , and ( 13 ) , we obtain , ... Page 35

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**cos**2 A = 1 -2 sin2 A , ( 76 )**cos**2 A = 2 cos2 A 1 . - ( 77 ) By means of ( 70 ) and ( 71 ) , we have 2**tan**A**tan**2 4 = 1 tan2 A ' ( 78 ) - 1 tan2 A cot 2 A = 2**tan**A ( 79 ) σ . 93. To find the**SINE**, & c . of**half**an angle by means of the ... Page 43

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**tangent of half**the sum of the opposite angles is to the**tangent of half**their difference . For , by ( 90 ) , a : b :: sin A : sin B ; whence ( Geom . , Prop . XII . Bk . II . ) , which a + ba - b :: sin A + sin B : sin A— sin B , may ... Page 46

... tan A b ) ( s s ( s — a ) C ; ( 109 ) tan B = ( 8 — a ) ( s —c ) ; ( 110 ) s ( s b ) tan C = - a ) ( s — b ) s ( s c ) ( 111 ) That is , The

... tan A b ) ( s s ( s — a ) C ; ( 109 ) tan B = ( 8 — a ) ( s —c ) ; ( 110 ) s ( s b ) tan C = - a ) ( s — b ) s ( s c ) ( 111 ) That is , The

**tangent of half**of any angle of a plane triangle is equal to the square root of half the sum of ... Page 57

... tan 1⁄2 ( A — B ) = tan † ( 4 + B ) = or , by logarithms , log tan ( A - B ) = log ( a - b ) —log ( a + b ) + log tan † ( A + B ) = log ( a — b ) — log ( a + b ) + log cot That is , - C. ( 133 ) The logarithmic

... tan 1⁄2 ( A — B ) = tan † ( 4 + B ) = or , by logarithms , log tan ( A - B ) = log ( a - b ) —log ( a + b ) + log tan † ( A + B ) = log ( a — b ) — log ( a + b ) + log cot That is , - C. ( 133 ) The logarithmic

**tangent of half**the ...### 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.