Elementary Mathematical Analysis: A Text Book for First Year College Students |
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abscissa algebraic amplitude arithmetical arithmetical progression axes called circle common logarithm complex number computation constant construction coördinate paper corresponding cos² cosine cubic yard cubical parabola curve decimal diagram diameter distance divided double scale draw ellipse equal Exercises exponential exponential function expression feet Find the equation formula geometrical progression given graph graphically harmonics Hence horizontal hyperbola inches inches of mercury intersection latus rectum length locus logarithm magnitude means motion multiplied negative operation ordinates parabola parametric equations perpendicular plane polar coördinates polar equation positive power function quadrant radians ratio rectangles rectangular coördinates represented root rotation seiche Show shown in Fig side sin² sine sinusoid slope Solve straight line student substituting tangent theorem tion trigonometric functions unit variable velocity vertical wave x-axis Y-axis zero ΙΟ
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Page 303 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 124 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Page 301 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides by the projection of the other upon that side.
Page 372 - Hence the quotient of two complex numbers is a complex number whose modulus is the quotient of the moduli, and whose amplitude is the difference of the amplitudes of the two complex numbers.
Page 227 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 302 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other...
Page 406 - A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line called a directrix.
Page 10 - ... function. A magnitude so related to another magnitude that for any value of one there is a corresponding value of the other. For instance, the area of a circle is a function of its radius. The radius is also a function of the area. functional reserves. The ability of the body to accomplish additional muscular or other activity and useful work beyond the normal level of activity of an individual.
Page 411 - Parabola is the locus of a point whose distance from a fixed point is always equal to its distance from a fixed straight line.
Page 125 - From the top of a vertical cliff, the angle of depression of a point on the shore 150 feet from the base of the cliff, is observed to be 30° : find the height of the cliff.