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 ix
... Greater than 45 ° . 215 140. Tables of Tangents and Secants .. 215 141. Formulæ of Verification .. 216 142. Tables of Logarithmic Trigonometric Functions .. 143. The Principle of Proportional Parts ... 217 218 ART . PAGE 144. To prove ...
... Greater than 45 ° . 215 140. Tables of Tangents and Secants .. 215 141. Formulæ of Verification .. 216 142. Tables of Logarithmic Trigonometric Functions .. 143. The Principle of Proportional Parts ... 217 218 ART . PAGE 144. To prove ...
Página 3
... greater than 2 , 4 , 8 , or any number of right angles . The line OA from which OB moves is called the initial line , and OB in its final position , the terminal line . The revolving line OB is called the generatrix . The point O is ...
... greater than 2 , 4 , 8 , or any number of right angles . The line OA from which OB moves is called the initial line , and OB in its final position , the terminal line . The revolving line OB is called the generatrix . The point O is ...
Página 4
... greater than one and less than two right angles , and is said to be an angle in the second quadrant . AOP , is greater than two and less than three right angles , and is said to be an angle in the third quadrant . AOP , is greater than ...
... greater than one and less than two right angles , and is said to be an angle in the second quadrant . AOP , is greater than two and less than three right angles , and is said to be an angle in the third quadrant . AOP , is greater than ...
Página 27
... greater than 90 ° , tan A changes from + ∞ to - ∞o . As A increases from 180 ° to 270 ° , MP increases from zero to OP , and is negative , OM decreases from OP to zero , and is negative ; therefore tan 270 ° = ∞ . Hence in the 3d ...
... greater than 90 ° , tan A changes from + ∞ to - ∞o . As A increases from 180 ° to 270 ° , MP increases from zero to OP , and is negative , OM decreases from OP to zero , and is negative ; therefore tan 270 ° = ∞ . Hence in the 3d ...
Página 28
... greater than unity . They are The secant and cosecant vary from 1 to -1 , passing through the value . They are never numerically less than unity . The tangent and cotangent are unlimited in value . They have all values from to + ∞ . 81 ...
... greater than unity . They are The secant and cosecant vary from 1 to -1 , passing through the value . They are never numerically less than unity . The tangent and cotangent are unlimited in value . They have all values from to + ∞ . 81 ...
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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.