Plane and Spherical TrigonometryD.C. Heath & Company, 1917 - 313 páginas |
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Página viii
... inverse function 78. Multiple values of an inverse function 79. Principal values • 80. Interpretation of sin sin - 1 a and sin - 1 sin a 74 74 75 77 77 81. Application of the fundamental relations to angles expressed as inverse ...
... inverse function 78. Multiple values of an inverse function 79. Principal values • 80. Interpretation of sin sin - 1 a and sin - 1 sin a 74 74 75 77 77 81. Application of the fundamental relations to angles expressed as inverse ...
Página 74
George Neander Bauer, William Ellsworth Brooke. CHAPTER VII INVERSE FUNCTIONS 76. Inverse trigonometric functions are closely related to the trigonometric functions previously studied . After introducing the fundamental idea of an inverse ...
George Neander Bauer, William Ellsworth Brooke. CHAPTER VII INVERSE FUNCTIONS 76. Inverse trigonometric functions are closely related to the trigonometric functions previously studied . After introducing the fundamental idea of an inverse ...
Página 75
... of a symbol for an inverse function . When a function is affected by 1 as an exponent , it must be written with parentheses , thus ( sin x ) -1 . 78. Multiple values of an inverse function . It has been shown that the trigonometric ...
... of a symbol for an inverse function . When a function is affected by 1 as an exponent , it must be written with parentheses , thus ( sin x ) -1 . 78. Multiple values of an inverse function . It has been shown that the trigonometric ...
Página 77
... of an inverse function is called its principal value , preference be- ing given to positive angles in case of ambiguity . The principal values of the inverse sine and the inverse cosecant lie between - π and 2 π ; of the inverse cosine and ...
... of an inverse function is called its principal value , preference be- ing given to positive angles in case of ambiguity . The principal values of the inverse sine and the inverse cosecant lie between - π and 2 π ; of the inverse cosine and ...
Página 78
... of a . This angle is evidently a , hence sin - 1 sin α = α , or more generally , sin - 1 sin α = n + ( − 1 ) " α . Similar relations exist between any direct function and the corresponding inverse function . Thus cos cos - 1 u = u ...
... of a . This angle is evidently a , hence sin - 1 sin α = α , or more generally , sin - 1 sin α = n + ( − 1 ) " α . Similar relations exist between any direct function and the corresponding inverse function . Thus cos cos - 1 u = u ...
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Términos y frases comunes
angle opposite angles of depression colog COMMON LOGARITHMS complex number computed cos a cos cos-¹ cos¹ cos² cos³ cot-¹ cot² cotangent coty csc² cube root decimal point determine difference Equating the real Find the height find the value flagpole four-place tables fundamental relations given angles greater than 90 Hence interpolation inverse function law of cosines law of sines law of tangents less than 180 line values Log Cot log sin ẞ loga logarithms of numbers mantissa Moivre's theorem negative number of degrees quadrant radians roots of unity sec-¹ sec² sides are given Similarly sin a cos sin a sin sin-¹ sin(a+b sin¹ sin² sin³ solution Solve the following spherical right triangle spherical triangle square root ẞ cot tan-¹ tan² tangent terminal line tower trigonometric functions Va² α α απ π π ייד
Pasajes populares
Página 4 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 130 - ... 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 4 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 111 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Página 3 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Página 85 - B is negative, and BD — — a cos B. The substitution of this in (4) leads us again to (3). Thus we see that (3) is true in all cases. THE LAW OF COSINES. The square of any side .of a plane triangle is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle. This may be regarded as a generalization of the Pythagorean Theorem to which it reduces when the included angle is a right angle. These two laws are among the most important of...
Página 2 - If the number is greater than 1, the characteristic is one less than the number of places to the left of the decimal point.
Página 131 - By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b...
Página 31 - The product of all the lines, that can be drawn from one of the angles of a regular polygon of n sides, inscribed in a circle whose radius is a, to all the other angular points = no.
Página 111 - From the top of a cliff 150 ft. high the angles of depression of the top and bottom of a tower are 30° and 60°, respectively.