Plane TrigonometryLongmans, Green, and Company, 1906 |
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Page 1
... calculations can be greatly lessened by the employment of a table of logarithms , an instrument which was invented for this very purpose by John Napier ( 1550-1617 ) , Baron of Merchiston in Scotland , and described by him in 1614. From ...
... calculations can be greatly lessened by the employment of a table of logarithms , an instrument which was invented for this very purpose by John Napier ( 1550-1617 ) , Baron of Merchiston in Scotland , and described by him in 1614. From ...
Page 6
... calculation . Special care is necessary in dealing with logarithms because of the fact that the mantissa is always positive , while the character- istic may be either positive or negative . Some typical examples involving negative ...
... calculation . Special care is necessary in dealing with logarithms because of the fact that the mantissa is always positive , while the character- istic may be either positive or negative . Some typical examples involving negative ...
Page 9
... calculation of straight and circular lines , angles , and areas belonging to figures on planes and spheres . It consists of two sections , viz . Plane Trigonometry and Spherical Trigonometry . Elementary trigonom- etry has many useful ...
... calculation of straight and circular lines , angles , and areas belonging to figures on planes and spheres . It consists of two sections , viz . Plane Trigonometry and Spherical Trigonometry . Elementary trigonom- etry has many useful ...
Page 11
... Calculate the following ratios , viz .: perpendicular hypotenuse base hypotenuse ' perpendicular base base hypotenuse hypotenuse perpendicular base perpendicular What are these ratios in a triangle whose base is 8. ] 11 RATIO . MEASURE ...
... Calculate the following ratios , viz .: perpendicular hypotenuse base hypotenuse ' perpendicular base base hypotenuse hypotenuse perpendicular base perpendicular What are these ratios in a triangle whose base is 8. ] 11 RATIO . MEASURE ...
Page 12
... calculate the ratios specified in Ex . 8. Calculate these ratios for a triangle whose base is 70 yd . , and perpendicular ... calculated values represent the true values of the numbers . In other words , the values of incommensurable num ...
... calculate the ratios specified in Ex . 8. Calculate these ratios for a triangle whose base is 70 yd . , and perpendicular ... calculated values represent the true values of the numbers . In other words , the values of incommensurable num ...
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Common terms and phrases
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
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