A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous ExamplesD.C. Heath & Company, 1892 - 368 páginas |
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Página 38
... integer , either positive or negative , the functions of n × 360 ° + A are the same as those of A. Thus the functions of 1470 ° the functions of 30 ° . If denotes any angle in circular measure , the functions of ( 2n + 0 ) are the same ...
... integer , either positive or negative , the functions of n × 360 ° + A are the same as those of A. Thus the functions of 1470 ° the functions of 30 ° . If denotes any angle in circular measure , the functions of ( 2n + 0 ) are the same ...
Página 40
... integer . - - a , and ( 1 ) Also the only negative angles which have the sine equal to a are ( a ) , and ( 2π - a ) , and the angles formed . by adding to these any multiple of four right angles taken negatively ; that is , we have 0 ...
... integer . - - a , and ( 1 ) Also the only negative angles which have the sine equal to a are ( a ) , and ( 2π - a ) , and the angles formed . by adding to these any multiple of four right angles taken negatively ; that is , we have 0 ...
Página 41
... integer . There- fore ( 3 ) is the general expression for all angles which have a given sine . NOTE . The same formula determines all the angles which have the same cosecant as a . 39. An Expression for All Angles with a Given Cosine a ...
... integer . There- fore ( 3 ) is the general expression for all angles which have a given sine . NOTE . The same formula determines all the angles which have the same cosecant as a . 39. An Expression for All Angles with a Given Cosine a ...
Página 42
... integer . - • ( 2 ) Now the angles in ( 1 ) and ( 2 ) may be arranged thus : 2n + α , ( 2n + 1 ) π + α , ( 2 n − 1 ) + α , ( 2 n − 2 ) + α , all of which , and no others , are included in the formula 0 = nπ + α , ( 3 ) where n is zero ...
... integer . - • ( 2 ) Now the angles in ( 1 ) and ( 2 ) may be arranged thus : 2n + α , ( 2n + 1 ) π + α , ( 2 n − 1 ) + α , ( 2 n − 2 ) + α , all of which , and no others , are included in the formula 0 = nπ + α , ( 3 ) where n is zero ...
Página 68
... integer . 2. Determine the limits between which A must lie to satisfy the equation 2 cos A = √1 + sin 2 A - V1 - sin 2 A. By ( 1 ) and ( 2 ) of Art . 53 , 2cos A can have this value only when cos A + sin A = √1 + sin 2A , and cos Asin ...
... integer . 2. Determine the limits between which A must lie to satisfy the equation 2 cos A = √1 + sin 2 A - V1 - sin 2 A. By ( 1 ) and ( 2 ) of Art . 53 , 2cos A can have this value only when cos A + sin A = √1 + sin 2A , and cos Asin ...
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Otras ediciones - Ver todas
A Treatise on Plane and Spherical Trigonometry: And Its Applications to ... Edward Albert Bowser Sin vista previa disponible - 2013 |
Términos y frases comunes
algebraically angle AOP angle of elevation base calculate centre circle circular measure common logarithms cos b cos cos² cosec cotangent decimal places denote diff equal equations EXAMPLES expression feet find log find the angle find the height find the number formulæ Given log Hence horizon hypotenuse integer log cot log sin log sine mantissa Multiply negative number whose logarithm observed obtained opposite perpendicular plane polar triangle positive Prove the following quadrant R₁ r₂ radian radius right angles right triangle sec² secant sides Similarly sin a cos sin B sin sin x sin² sin³ sines and cosines sinx siny solution Solve spherical triangle subtends table of logarithms table of natural tan² tangent triangle ABC trigonometric functions vertical yards ОР
Pasajes populares
Página 148 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 147 - Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles.
Página 278 - AB'C, we have by (4) cos a' — cos b cos c' + sin b sin c' cos B'AC, or cos(тг— a) = cos b cos(тг— c) + sin b sin(тт — C)COS(тг —A). .-. cos a = cos b cos с + sin b sin с cos A.
Página 278 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 278 - 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...
Página 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 17 - If the cosine of A be subtracted from unity, the remainder is called the versed sine of A. If the sine of A be...
Página 89 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 149 - 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.