Plane TrigonometryLongmans, Green, and Company, 1906 |
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Page 2
... equal N. For some purposes , this idea is presented in these words : If a = N , then x is the logarithm of N to the base a . The latter statement is taken as the definition of a logarithm , and is expressed by mathematical symbols in ...
... equal N. For some purposes , this idea is presented in these words : If a = N , then x is the logarithm of N to the base a . The latter statement is taken as the definition of a logarithm , and is expressed by mathematical symbols in ...
Page 3
... equal to the sum of the logarithms of the factors . ( 2 ) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator diminished by the logarithm of the denominator . ( 3 ) The logarithm of the rth power of a ...
... equal to the sum of the logarithms of the factors . ( 2 ) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator diminished by the logarithm of the denominator . ( 3 ) The logarithm of the rth power of a ...
Page 4
... equal to 1th of the logarithm of the number . Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and division are replaced by those ...
... equal to 1th of the logarithm of the number . Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and division are replaced by those ...
Page 13
... equal to the sum of the squares of the measures of the other two sides . ( b ) The ratio of the length of any circle to its diameter is a number which is the same for all circles . * The exact value of this ratio is incommensurable and ...
... equal to the sum of the squares of the measures of the other two sides . ( b ) The ratio of the length of any circle to its diameter is a number which is the same for all circles . * The exact value of this ratio is incommensurable and ...
Page 15
... equal to 39.37 . . . inches . * Drawing to scale . It is often desirable to have a drawing on paper which shall serve to give an accurate idea of the relations of certain lines and positions . Maps and architects ' plans are familiar ...
... equal to 39.37 . . . inches . * Drawing to scale . It is often desirable to have a drawing on paper which shall serve to give an accurate idea of the relations of certain lines and positions . Maps and architects ' plans are familiar ...
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Common terms and phrases
A+B+C acute angle algebraic centre CHAPTER circumscribing computation cosē cosec cotangent deduced denoted Derive diedral angle draw equal equator EXAMPLES expression figure Find the distance formulas geometry given Hence hypotenuse included angle inscribed circle intersection latitude law of cosines law of sines length logarithms mantissa mathematics meridian method NOTE number of degrees number of sides opposite perpendicular plane triangle Plane Trigonometry polar triangle pole positive quadrant radian measure radii radius regular polygon relations respectively right angles right triangles right-angled triangle secant Show sides and angles sinē solid angle solution Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tables tanē tangent terminal line three angles tower triangle ABC trigono trigonometric functions trigonometric ratios π π
Popular passages
Page 52 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Page 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 108 - 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...
Page 74 - The area of the surface of a sphere is four times the area of a great circle.
Page 108 - 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.
Page 72 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 62 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area, F THE RIGHT TRIANGLE.
Page 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 200 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Page 202 - Find the area of a regular polygon of n sides inscribed in a circle, and show, by increasing the number of sides of the polygon without limit, how the expression for the area of the circle may be obtained. 13. (a) Find the distance at which a building 50 ft. wide will subtend an angle of 3'. (6) A church spire 45 ft. high subtends an angle of 9