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 1
... tions of them called the trigonometric functions . Plane Trigonometry comprises the solution of plane trian- gles and investigations of plane angles and their functions . Trigonometry was originally the science which treated only of the ...
... tions of them called the trigonometric functions . Plane Trigonometry comprises the solution of plane trian- gles and investigations of plane angles and their functions . Trigonometry was originally the science which treated only of the ...
Página 17
... tions of an angle A are written thus : sin A , cos A , tan A , cot A , sec A , cosec A , vers A , covers A. The following is the verbal enunciation of these defini- tions : The sine of an angle is the ratio of the opposite side to the ...
... tions of an angle A are written thus : sin A , cos A , tan A , cot A , sec A , cosec A , vers A , covers A. The following is the verbal enunciation of these defini- tions : The sine of an angle is the ratio of the opposite side to the ...
Página 24
... tions of the trigonometric functions Α Quad . B P 2nd 1st Quad . Quadrant P M M 3rd M A M 4th Quad . P are B MP sin A OM = cos A = tan A MP OP ' OP 2 = OM ' ОР sec A OM = cot A OP = OM ' " cosec A = MP ' MP B Α A M I. When A lies in the ...
... tions of the trigonometric functions Α Quad . B P 2nd 1st Quad . Quadrant P M M 3rd M A M 4th Quad . P are B MP sin A OM = cos A = tan A MP OP ' OP 2 = OM ' ОР sec A OM = cot A OP = OM ' " cosec A = MP ' MP B Α A M I. When A lies in the ...
Página 31
... tions of 60 ° and 30 ° . —Let AB be an equilateral triangle . Draw AD perpen- dicular to BC . Then AD bisects the angle BAC and the side BC . Therefore BAD = 30 ° , and ABD = 60 ° . 2 m B m Let BA = 2m . .. BD : = m RELATIONS BETWEEN ...
... tions of 60 ° and 30 ° . —Let AB be an equilateral triangle . Draw AD perpen- dicular to BC . Then AD bisects the angle BAC and the side BC . Therefore BAD = 30 ° , and ABD = 60 ° . 2 m B m Let BA = 2m . .. BD : = m RELATIONS BETWEEN ...
Página 61
... 2x , and sin 2x . 50. To Express the Functions of 3x in Terms of the Func- tions of x . Put y = 2x in ( 1 ) of Art . 42 , and it becomes sin 3x sin ( 2x + x ) = = EXAMPLES . 61 Functions of 3 x in Terms of the Functions of x.
... 2x , and sin 2x . 50. To Express the Functions of 3x in Terms of the Func- tions of x . Put y = 2x in ( 1 ) of Art . 42 , and it becomes sin 3x sin ( 2x + x ) = = EXAMPLES . 61 Functions of 3 x in Terms of the Functions of x.
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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.