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 22
... similarly for the other functions . PC , AT , Therefore , in a circle whose radius is unity , the Trigono- metric functions of an arc , or of the angle at the centre meas- ured by that arc , may be defined as follows : The sine is the ...
... similarly for the other functions . PC , AT , Therefore , in a circle whose radius is unity , the Trigono- metric functions of an arc , or of the angle at the centre meas- ured by that arc , may be defined as follows : The sine is the ...
Página 30
... Similarly , any one of the functions of an angle may be expressed in terms of any other function of that angle . The sign of the radical will in all cases depend upon the quadrant in which the angle ◊ lies . 25. Graphic Method of ...
... Similarly , any one of the functions of an angle may be expressed in terms of any other function of that angle . The sign of the radical will in all cases depend upon the quadrant in which the angle ◊ lies . 25. Graphic Method of ...
Página 31
... similarly the other functions may be expressed in terms of cosec A. 26. To find the Trigonometric Functions of 45 ° . - Let ABC be an isosceles right triangle in which Then Let Then CA = CB . CAB CBA = 45 ° . = AC = m = CB . AB AC2 + ...
... similarly the other functions may be expressed in terms of cosec A. 26. To find the Trigonometric Functions of 45 ° . - Let ABC be an isosceles right triangle in which Then Let Then CA = CB . CAB CBA = 45 ° . = AC = m = CB . AB AC2 + ...
Página 34
... Similarly , tan ( 90 ° — A ) = tan AOP'- = = = OP ' OP cot A. The other relations are obtained by inverting the above . 30. Functions of Supplemental An- - gles . Let OP and OP ' be the positions of the radius for any angle AOP = A ...
... Similarly , tan ( 90 ° — A ) = tan AOP'- = = = OP ' OP cot A. The other relations are obtained by inverting the above . 30. Functions of Supplemental An- - gles . Let OP and OP ' be the positions of the radius for any angle AOP = A ...
Página 35
... Similarly the other relations may be obtained . 31. To prove sin ( 90 ° + A ) = cos A , cos ( 90 ° + A ) = — sin A , and tan ( 90 ° + A ) = - cot A. Let OP and OP ' be the positions of the radius for any angle AOP = A , and AOP ' 90 ° + ...
... Similarly the other relations may be obtained . 31. To prove sin ( 90 ° + A ) = cos A , cos ( 90 ° + A ) = — sin A , and tan ( 90 ° + A ) = - cot A. Let OP and OP ' be the positions of the radius for any angle AOP = A , and AOP ' 90 ° + ...
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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.