The elements of plane trigonometry |
Dentro del libro
Resultados 1-5 de 27
Página vii
... EXPRESSIONS INTO FACTORS . 134. To solve a quadratic equation ........ 135 , 136. To solve a cubic equation .. PAGE 128 131 n - 137-140 . To resolve x2 - 1 , x2 ” +1 , x2 ′′ + 1 − 1 , x2 + 1 + 1 , into quadratic factors .. 133 141. To ...
... EXPRESSIONS INTO FACTORS . 134. To solve a quadratic equation ........ 135 , 136. To solve a cubic equation .. PAGE 128 131 n - 137-140 . To resolve x2 - 1 , x2 ” +1 , x2 ′′ + 1 − 1 , x2 + 1 + 1 , into quadratic factors .. 133 141. To ...
Página 11
... expression of calculation is called a function of a quantity , if its value depend in any manner on the value of that quantity . Since the magnitudes of the sine , the cosine , the tangent , & c . of an angle depend on the magnitude of ...
... expression of calculation is called a function of a quantity , if its value depend in any manner on the value of that quantity . Since the magnitudes of the sine , the cosine , the tangent , & c . of an angle depend on the magnitude of ...
Página 17
... expressions . ( 1 ) Tan A = ( 2 ) Sec A = NC NC AC AN AC AN = = ... cos A = AN AC 1 AN AC 1 sec A sin A = cos A H 1 cos A AN AN ( 3 ) Cot A = = NC NC AC = COS A sin A B ' AC AN 1 1 ( 4 ) Cot A = = = D ' NC NC tan A AN 1 .. tan A = ( 5 ) ...
... expressions . ( 1 ) Tan A = ( 2 ) Sec A = NC NC AC AN AC AN = = ... cos A = AN AC 1 AN AC 1 sec A sin A = cos A H 1 cos A AN AN ( 3 ) Cot A = = NC NC AC = COS A sin A B ' AC AN 1 1 ( 4 ) Cot A = = = D ' NC NC tan A AN 1 .. tan A = ( 5 ) ...
Página 18
... expressions proved in the last Article we can find the value of any one of the quantities defined in Art . 15 , in terms of any other of those quantities . ( 1 ) Tan A = sin A √1 − ( sin 4 ) 2 ( 2 ) sin A For tan 4 = cos A , Art . 27 ...
... expressions proved in the last Article we can find the value of any one of the quantities defined in Art . 15 , in terms of any other of those quantities . ( 1 ) Tan A = sin A √1 − ( sin 4 ) 2 ( 2 ) sin A For tan 4 = cos A , Art . 27 ...
Página 33
... expression becomes , - tan ( 45o + A ) – tan ( 45o — A ) = 2 tan 2 A ... ........ ( 6 ) . - tan Atan B sin ( A + B ) = 44 . To shew that tan Atan B sin ( A - B ) sin A sin B + tan A + tan B cos A cos B = tan Atan B sin A sin B cos A cos ...
... expression becomes , - tan ( 45o + A ) – tan ( 45o — A ) = 2 tan 2 A ... ........ ( 6 ) . - tan Atan B sin ( A + B ) = 44 . To shew that tan Atan B sin ( A - B ) sin A sin B + tan A + tan B cos A cos B = tan Atan B sin A sin B cos A cos ...
Otras ediciones - Ver todas
Términos y frases comunes
A₁ AC AC angle containing Asin base C₁ centre circle coefficient cosec cosines decimal determined Diff difference digit equal errors Eucl expression formulæ given goniometric functions greater Hence increment integer last Article less m₁ magnitude mantissa measured Napier's rules nearly negative number of seconds P₁ perpendicular plane triangle planes AOB polar triangle pole polygon positive proved quantity radius Regular Polyhedron right angles right-angled triangle S₁ secants shew shewn Similarly sin A sin sines sines and cosines small angle solid angle sphere spherical excess spherical triangle SPHERICAL TRIGONOMETRY subtended subtraction tabular logarithmic tangents THEOREM triangle ABC triangle whose sides TRIGONOMETRY versin Wherefore π π
Pasajes populares
Página 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.
Página 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.
Página 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.
Página 57 - ... the three interior angles of a triangle are together equal to two right angles.
Página 12 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.
Página 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.
Página 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.