Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página xi
... quadrants 42. To represent the angle geometrically when the ratios are given 43. Connection between angles and trigonometric ratios 44. Relations between the trigonometric ratios of an angle 45. Ratios of 90 ° — A , 90 ° + A , 180 ° – A ...
... quadrants 42. To represent the angle geometrically when the ratios are given 43. Connection between angles and trigonometric ratios 44. Relations between the trigonometric ratios of an angle 45. Ratios of 90 ° — A , 90 ° + A , 180 ° – A ...
Página 50
... quadrant . When an object is above the observer's eye , the angle between the line from the eye to the object , and the horizontal line through the eye and in the same vertical plane as the first line , is called the angle of elevation ...
... quadrant . When an object is above the observer's eye , the angle between the line from the eye to the object , and the horizontal line through the eye and in the same vertical plane as the first line , is called the angle of elevation ...
Página 69
... quadrant ; when the final position of the turning line is between OY and OX1 , the angle described is said to be in the sec- ond quadrant ; and so on for the third and fourth quadrants . - - - For example , the angles 30 ° , 345 ° , 395 ...
... quadrant ; when the final position of the turning line is between OY and OX1 , the angle described is said to be in the sec- ond quadrant ; and so on for the third and fourth quadrants . - - - For example , the angles 30 ° , 345 ° , 395 ...
Página 71
... quadrant ; the second figure represents any angle in the second quadrant ; the third figure , any angle in the third quadrant ; and the fourth figure , any angle in the fourth quadrant . In each figure the angle will be called A. M X х ...
... quadrant ; the second figure represents any angle in the second quadrant ; the third figure , any angle in the third quadrant ; and the fourth figure , any angle in the fourth quadrant . In each figure the angle will be called A. M X х ...
Página 72
... quadrants , it will be seen that the ratios of the angles in these quadrants are posi- tive or negative , as indicated in the following table : 41. ] ALGEBRAIC SIGNS OF RATIOS . QUADRANT . Sine 72 [ CH . V. PLANE TRIGONOMETRY .
... quadrants , it will be seen that the ratios of the angles in these quadrants are posi- tive or negative , as indicated in the following table : 41. ] ALGEBRAIC SIGNS OF RATIOS . QUADRANT . Sine 72 [ CH . V. PLANE TRIGONOMETRY .
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Términos y frases comunes
A+B+C acute angles algebraic centre CHAPTER circumscribing computation construction cos² cosec cosine cotangent deduced definitions denoted derived diedral angle draw equal equation EXAMPLES expression figure formulas geometry height Hence hypotenuse included angle inscribed circle intersection isosceles triangle law of cosines law of sines length logarithms M₁ method negative NOTE number of degrees number of sides OP₁ opposite perpendicular Plane Trigonometry polar triangle pole positive angles quadrant QUESTIONS AND EXERCISES radian measure radius regular polygon relations respectively revolving right angles right-angled triangle sec² secant Show shown sides and angles sin² sine solid angle Solve ABC sphere spherical angle spherical degrees spherical excess spherical polygon spherical triangle spherical trigonometry subtended tan² tangent terminal line tower triangle ABC triedral trigono trigonometric functions trigonometric ratios whole number
Pasajes populares
Página 35 - 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 25 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 87 - 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 85 - 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 55 - 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 111 - The ratio of a circumference of a circle to its diameter is the same for all circles. [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance, to Euclid VI., 33.* The proof of (6) is not contained in all geometries ; for instance, Euclid does not give...
Página 183 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Página 41 - 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.