Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of Computation, Volumen1H. Holt, 1882 - 168 páginas |
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Página
... quadrants , 22. Special values of the trigonometric func- tions , 26. Angles corresponding to given functions , 27. Relations between the six trigonometric functions , 30 . CHAPTER III . OF RIGHT TRIANGLES .... Fundamental relations ...
... quadrants , 22. Special values of the trigonometric func- tions , 26. Angles corresponding to given functions , 27. Relations between the six trigonometric functions , 30 . CHAPTER III . OF RIGHT TRIANGLES .... Fundamental relations ...
Página 2
... quadrant or right angle = 90 ° . This is called the sexagesimal division of the circle . 5. The Centesimal Division . The sexagesimal division of the circle is by no means so convenient as one in which each unit is 10 times or 100 times ...
... quadrant or right angle = 90 ° . This is called the sexagesimal division of the circle . 5. The Centesimal Division . The sexagesimal division of the circle is by no means so convenient as one in which each unit is 10 times or 100 times ...
Página 5
... quadrant . second " 66 66 66 90 ° 66 180 ° 66 66 66 66 66 180 ° " 270 ° 66 " third 66 66 66 66 270 ° " 360 ° 66 " fourth 66 Counting the angles negatively from OA , An angle between - 0 ° and 90 ° is in the fourth quadrant . 66 66 66 90 ...
... quadrant . second " 66 66 66 90 ° 66 180 ° 66 66 66 66 66 180 ° " 270 ° 66 " third 66 66 66 66 270 ° " 360 ° 66 " fourth 66 Counting the angles negatively from OA , An angle between - 0 ° and 90 ° is in the fourth quadrant . 66 66 66 90 ...
Página 6
... quadrants will the respective multi- ples fall , and what will be the smallest positive measures of the several angles formed ? - - 8. Show that the following pairs of angles are supplementary : 90 ° + x and 90 ° - x ; 270 ° x and 270 ...
... quadrants will the respective multi- ples fall , and what will be the smallest positive measures of the several angles formed ? - - 8. Show that the following pairs of angles are supplementary : 90 ° + x and 90 ° - x ; 270 ° x and 270 ...
Página 8
... quadrant , what are the limits be- tween which its bisectors must fall ? 7. Between what three sets of limits must a be contained in order that 3a may fall in the fourth quadrant ? 8. Show that while one sixth of the general measure of ...
... quadrant , what are the limits be- tween which its bisectors must fall ? 7. Between what three sets of limits must a be contained in order that 3a may fall in the fourth quadrant ? 8. Show that while one sixth of the general measure of ...
Términos y frases comunes
algebraic signs angle AOB angle XOM axes base circle circumference coefficients compute cos² cos³ cosec cosine cotangent distance divided equal example EXERCISES expression find the angles find the remaining find the values formulæ given gives Hence hypothenuse imaginary unit intersect latitude line OX measure metres negative nth roots obtain opposite angles parallel parallelogram perpendicular polar triangle pole polygon positive direction preceding problem quantities radius rectangular co-ordinates right angle right triangle roots of unity secant sin a cos sin a sin sin² sine sines and cosines Solution spherical triangle spherical trigonometry squares straight line substituting subtract supplementary angles suppose three angles three rectangular planes three sides tion trapezoid trigonometric functions trihedral angle vertex zero
Pasajes populares
Página 66 - 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 139 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 132 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.
Página 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 66 - IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle...
Página 105 - ... the modulus of a product is equal to the product of the moduli of the factors.
Página 43 - At the top of a tower, 108 feet high, the angles of depression of the top and bottom of...
Página 73 - The area of a triangle is equal to half the product of any two of its sides multiplied by the sine of the included angle, radius being unity.