A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous ExamplesD.C. Heath & Company, 1892 - 368 páginas |
Dentro del libro
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Página vii
... is Given 112 112 114 80. To find the Angle whose Logarithmic Cosine is Given . 81. Angles near the Limits of the Quadrant Examples . 115 116 117 CHAPTER V. SOLUTION OF TRIGONOMETRIC EQUATIONS . ᎪᎡᎢ . 82. CONTENTS . vii.
... is Given 112 112 114 80. To find the Angle whose Logarithmic Cosine is Given . 81. Angles near the Limits of the Quadrant Examples . 115 116 117 CHAPTER V. SOLUTION OF TRIGONOMETRIC EQUATIONS . ᎪᎡᎢ . 82. CONTENTS . vii.
Página ix
... Limit of is Unity .. 209 134. Limiting Values of sin ✪ and cos 0 . 209 135. To calculate the Sine and Cosine of 10 " and of 1 ' . 211 136. To construct a Table of Natural Sines and Cosines .. 137. Another Method .. 213 213 138. The ...
... Limit of is Unity .. 209 134. Limiting Values of sin ✪ and cos 0 . 209 135. To calculate the Sine and Cosine of 10 " and of 1 ' . 211 136. To construct a Table of Natural Sines and Cosines .. 137. Another Method .. 213 213 138. The ...
Página 67
... limits between which A must lie to satisfy the equation 2 sin A√1 + sin 2A - √1 - sin 2 A. By ( 1 ) and ( 2 ) of Art . 53 , 2 sin A can have this value . only when sin A + cos A = √1 + sin 2 A , - and sin A - cos A = - √1 - sin2 A ...
... limits between which A must lie to satisfy the equation 2 sin A√1 + sin 2A - √1 - sin 2 A. By ( 1 ) and ( 2 ) of Art . 53 , 2 sin A can have this value . only when sin A + cos A = √1 + sin 2 A , - and sin A - cos A = - √1 - sin2 A ...
Página 68
... 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 A == - √1 − sin 2 A ...
... 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 A == - √1 − sin 2 A ...
Página 69
... limits between which A must lie when 2 sin A = √1 + sin 2 A - √1 - sin 2 A. 56. Find the Values of the Functions of 22. - In ( 3 ) , ( 4 ) , and ( 5 ) of Art . 51 , put x = 45 ° . Then 1 sin 2210 = cos 45 ° 2 √2 - √2 2 cos 221 ° = 1 ...
... limits between which A must lie when 2 sin A = √1 + sin 2 A - √1 - sin 2 A. 56. Find the Values of the Functions of 22. - In ( 3 ) , ( 4 ) , and ( 5 ) of Art . 51 , put x = 45 ° . Then 1 sin 2210 = cos 45 ° 2 √2 - √2 2 cos 221 ° = 1 ...
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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.