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 5
... formed by any number of complete revolutions , either in the positive direction added to the positive angle AOP , or in the negative direction added to the negative angle AOP . In all cases the angle is said to be in the quadrant ...
... formed by any number of complete revolutions , either in the positive direction added to the positive angle AOP , or in the negative direction added to the negative angle AOP . In all cases the angle is said to be in the quadrant ...
Página 16
... forming a right triangle ABC , right - angled at C. Then denot- ing the angles by the capital letters A , B , C , respectively , and the three sides A C b -R opposite these angles by the corresponding small italics , a , b , c , * we ...
... forming a right triangle ABC , right - angled at C. Then denot- ing the angles by the capital letters A , B , C , respectively , and the three sides A C b -R opposite these angles by the corresponding small italics , a , b , c , * we ...
Página 23
... happens to be . Let AOP be an angle of any mag- nitude formed POSITIVE AND NEGATIVE LINES . 23 Representation of the Functions by Straight Lines Positive and Negative Lines ART PAGE 18 Functions of Angles of Any Magnitude.
... happens to be . Let AOP be an angle of any mag- nitude formed POSITIVE AND NEGATIVE LINES . 23 Representation of the Functions by Straight Lines Positive and Negative Lines ART PAGE 18 Functions of Angles of Any Magnitude.
Página 24
... formed by OP revolving from an initial position OA . Draw PM to AA ' . Consider OP as always positive . Let the angle AOP be denoted by A ; then whatever be the magnitude of the angle A , the defini- tions of the trigonometric functions ...
... formed by OP revolving from an initial position OA . Draw PM to AA ' . Consider OP as always positive . Let the angle AOP be denoted by A ; then whatever be the magnitude of the angle A , the defini- tions of the trigonometric functions ...
Página 40
... formed by adding any multiple of four right angles to a and π — α . Hence , if be the general value of the required angle , we have 0 = 2nπ + α , or 0 = 2 nя + π- - α , where n is zero or any positive integer . - - a , and ( 1 ) Also ...
... formed by adding any multiple of four right angles to a and π — α . Hence , if be the general value of the required angle , we have 0 = 2nπ + α , or 0 = 2 nя + π- - α , where n is zero or any positive integer . - - a , and ( 1 ) Also ...
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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.