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 viii
... centre and the Circumcentre . 106. To find the Area of a Cyclic Quadrilateral ... 155 157 Examples .. 159 CHAPTER VII . SOLUTION OF TRIANGLES . 107. Definitions . 165 108. Four Cases of Right Triangles .. 165 ART . Given a Side and the ...
... centre and the Circumcentre . 106. To find the Area of a Cyclic Quadrilateral ... 155 157 Examples .. 159 CHAPTER VII . SOLUTION OF TRIANGLES . 107. Definitions . 165 108. Four Cases of Right Triangles .. 165 ART . Given a Side and the ...
Página 3
... b ) . The revolving line is always considered negative . A 5. The Measure of Angles . An angle is measured by the arc of a circle whose centre is at the vertex of the angle and whose ends are on the sides of the THE CIRCULAR MEASURE . 3.
... b ) . The revolving line is always considered negative . A 5. The Measure of Angles . An angle is measured by the arc of a circle whose centre is at the vertex of the angle and whose ends are on the sides of the THE CIRCULAR MEASURE . 3.
Página 4
... centre A is O. The two perpendicular diam- eters AA ' and BB ' of this circle will inclose the four right angles AOB , BOA ' , A'OB ' , and B'OA . B The circumference is divided at the points A , B , A ' , B ' into four quadrants , of ...
... centre A is O. The two perpendicular diam- eters AA ' and BB ' of this circle will inclose the four right angles AOB , BOA ' , A'OB ' , and B'OA . B The circumference is divided at the points A , B , A ' , B ' into four quadrants , of ...
Página 6
... centre of a circle by an arc equal in length to the radius . This unit of circular measure is called a radian . B radian Let O be the centre of a circle whose radius is r . Let the arc AB be equal to the radius OA = r . Then , since ...
... centre of a circle by an arc equal in length to the radius . This unit of circular measure is called a radian . B radian Let O be the centre of a circle whose radius is r . Let the arc AB be equal to the radius OA = r . Then , since ...
Página 15
... centre of a circle of radius 25 feet , which intercepts an arc of 37 feet . Ans . 11 . 42. Find the number of degrees in an angle at the centre of a circle of radius 10 feet , which intercepts an arc of 5π feet . Ans . 90 ° . 43. Find ...
... centre of a circle of radius 25 feet , which intercepts an arc of 37 feet . Ans . 11 . 42. Find the number of degrees in an angle at the centre of a circle of radius 10 feet , which intercepts an arc of 5π feet . Ans . 90 ° . 43. Find ...
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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.