Plane and Spherical TrigonometryD.C. Heath & Company, 1917 - 313 páginas |
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Página vi
... Definitions of the trigonometric functions 22. Values of the trigonometric functions of 30 ° , 45 ° , and 60 ° 23. Values of the trigonometric functions of 120 ° , 135 ° , and 150 ° 24. Signs of the trigonometric ratios • 25 ...
... Definitions of the trigonometric functions 22. Values of the trigonometric functions of 30 ° , 45 ° , and 60 ° 23. Values of the trigonometric functions of 120 ° , 135 ° , and 150 ° 24. Signs of the trigonometric ratios • 25 ...
Página x
... Definition of spherical right triangle 127. Formulas for the solution of right triangles . 128. Direct geometric derivation of formulas 129. Sufficiency of formulas . · • PAGE • 132 • 132 · 133 134 134 134 137 130. Comparison of ...
... Definition of spherical right triangle 127. Formulas for the solution of right triangles . 128. Direct geometric derivation of formulas 129. Sufficiency of formulas . · • PAGE • 132 • 132 · 133 134 134 134 137 130. Comparison of ...
Página 1
... definitions of trigonometry . RECTANGULAR COORDINATES 2. Directed lines . A positive and a negative direction . may be assigned arbitrarily to every line . If the direction from A to C is positive , the opposite direction from C to A is ...
... definitions of trigonometry . RECTANGULAR COORDINATES 2. Directed lines . A positive and a negative direction . may be assigned arbitrarily to every line . If the direction from A to C is positive , the opposite direction from C to A is ...
Página 8
... definition of a radian that if any arc of a circle AB be divided by the radius , the quotient indicates the number of radians contained in the central angle subtended by the given arc , hence 8 Α r = angle AOB arc AB radius = the length ...
... definition of a radian that if any arc of a circle AB be divided by the radius , the quotient indicates the number of radians contained in the central angle subtended by the given arc , hence 8 Α r = angle AOB arc AB radius = the length ...
Página 12
... Definitions of the trigonometric functions . Let OX and OP be the initial and terminal lines respectively of any angle α . X ' r P r α y y α 88 х A X X'A 30 х X A x X'y ХА X X ' y X r r P Let P be any point on the terminal line , OP or ...
... Definitions of the trigonometric functions . Let OX and OP be the initial and terminal lines respectively of any angle α . X ' r P r α y y α 88 х A X X'A 30 х X A x X'y ХА X X ' y X r r P Let P be any point on the terminal line , OP or ...
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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.