Plane TrigonometryLongmans, Green, and Company, 1906 |
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Página xii
... Changes in the trigonometric functions as the angle increases from 0 ° to 360 ° 131 · 78. Periodicity of the trigonometric functions 134 79. The old or line definitions of the trigonometric functions 80. Geometrical representation of ...
... Changes in the trigonometric functions as the angle increases from 0 ° to 360 ° 131 · 78. Periodicity of the trigonometric functions 134 79. The old or line definitions of the trigonometric functions 80. Geometrical representation of ...
Página 5
... change is made in the position of the decimal point in a number , the value of the number is changed by some integral power of 10. Its logarithm is then changed by a whole number only , and , consequently , its mantissa is not affected ...
... change is made in the position of the decimal point in a number , the value of the number is changed by some integral power of 10. Its logarithm is then changed by a whole number only , and , consequently , its mantissa is not affected ...
Página 18
... amount of labour that would be necessary in order to change the mathematical tables computed for the other system . = = NOTE 3. The sexagesimal system ( from sexagesimus 18 [ CH . II . PLANE TRIGONOMETRY . Degree measure The protractor.
... amount of labour that would be necessary in order to change the mathematical tables computed for the other system . = = NOTE 3. The sexagesimal system ( from sexagesimus 18 [ CH . II . PLANE TRIGONOMETRY . Degree measure The protractor.
Página 76
... changes when the angle changes . The same can be shown for the other ratios . Hence , ( 2 ) The ratios of an angle change when the angle changes . The variation in the ratios as the angle increases , is discussed in Art . 77 . Ex . 1 ...
... changes when the angle changes . The same can be shown for the other ratios . Hence , ( 2 ) The ratios of an angle change when the angle changes . The variation in the ratios as the angle increases , is discussed in Art . 77 . Ex . 1 ...
Página 90
... change A into 90 ° - A ; then sin ( 90 ° — A + B ) = sin ( 90 ° — A ) cos B + cos ( 90 ° — A ) sin B. From this , sin ( 90 ° — A — B ) , i.e. cos ( A — B ) = cos A cos B + sin A sin B. In ( 1 ) Art . 46 , change B into ( — B ) ; then ...
... change A into 90 ° - A ; then sin ( 90 ° — A + B ) = sin ( 90 ° — A ) cos B + cos ( 90 ° — A ) sin B. From this , sin ( 90 ° — A — B ) , i.e. cos ( A — B ) = cos A cos B + sin A sin B. In ( 1 ) Art . 46 , change B into ( — B ) ; then ...
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Términos y frases comunes
A+B+C acute angle algebraic centre CHAPTER circumscribing computation cos² 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 sin² solid angle solution Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tables tan² tangent terminal line three angles tower triangle ABC trigono trigonometric functions trigonometric ratios π π
Pasajes populares
Página 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...
Página 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 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...
Página 74 - The area of the surface of a sphere is four times the area of a great circle.
Página 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.
Página 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...
Página 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.
Página 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 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.
Página 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