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 4
... figure , the angle AOP1 , between the initial line OA and the revolving line OP1 , is less than a right angle , and is said to be an angle in the first quadrant . AOP , is greater than one and less than two right angles , and is said to ...
... figure , the angle AOP1 , between the initial line OA and the revolving line OP1 , is less than a right angle , and is said to be an angle in the first quadrant . AOP , is greater than one and less than two right angles , and is said to ...
Página 15
... circle to its diameter . Ans . 3.1416 . 50. Find the number of radians in 10 " correct to four sig- nificant figures ( use for π ) . Ans . .00004848 . 35 CHAPTER II . THE TRIGONOMETRIC FUNCTIONS . - B D EXAMPLES . 15.
... circle to its diameter . Ans . 3.1416 . 50. Find the number of radians in 10 " correct to four sig- nificant figures ( use for π ) . Ans . .00004848 . 35 CHAPTER II . THE TRIGONOMETRIC FUNCTIONS . - B D EXAMPLES . 15.
Página 26
... figure of Art . 19 cos A = OM OP When the angle A is 0 ° , P coincides with A , and OM = OP ; therefore cos 0 ° = 1 . As A increases from 0 ° to 90 ° , OM decreases from OP to . zero and is positive ; therefore cos 90 ° = 0 . Hence in ...
... figure of Art . 19 cos A = OM OP When the angle A is 0 ° , P coincides with A , and OM = OP ; therefore cos 0 ° = 1 . As A increases from 0 ° to 90 ° , OM decreases from OP to . zero and is positive ; therefore cos 90 ° = 0 . Hence in ...
Página 27
... figure of Art . 19 MP tan A = • OM When A is 0 ° , MP is zero , and OM 0 ° = 0 . = OP ; therefore tan As A increases from 0 ° to 90 ° , MP increases from zero to OP , and OM decreases from OP to zero , so that on both accounts tan A ...
... figure of Art . 19 MP tan A = • OM When A is 0 ° , MP is zero , and OM 0 ° = 0 . = OP ; therefore tan As A increases from 0 ° to 90 ° , MP increases from zero to OP , and OM decreases from OP to zero , so that on both accounts tan A ...
Página 38
... figure of Art . 18 ; then if OP revolve in the positive or the negative direction through an angle of 360 ° , it will return to the position from which it started . Hence it is clear from the definitions that the trigonometric functions ...
... figure of Art . 18 ; then if OP revolve in the positive or the negative direction through an angle of 360 ° , it will return to the position from which it started . Hence it is clear from the definitions that the trigonometric functions ...
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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.