A short course in college mathematics; comprising thirty-six lessons on algebra, coordinate methods, and plane trigonometry

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 edition. Excerpt: ...equation of the form f(x, y) + k-jx, y) = 0, k being any constant, passes through all the intersection points of Ci and C2. 19. What is meant by a linear equation? When are two linear equations inconsistent? 20. Show how the real roots of every quadratic equation 'ax2 + bx + c 0 can be found graphically by means of the unit parabola and some straight line. 21. Show how the real roots of every cubic equation in x can be found graphically by means of the cubical parabola y = x3 and some straight line. 22. Show how the real roots of every quartic equation in x can be found graphically by means of the unit parabola and some circle. 23. When are two sets of simultaneous equations said to be equivalent? Interpret this condition graphically. 24. Is the graphic method of solving equations of any practical value? Illustrate by an example. CHAPTER III TRIGONOMETRIC FUNCTIONS LESSON XVII--THE GENERAL ANGLE AND ITS MEASURES 17.1. Definition of an Angle. In elementary geometry an angle is frequently defined as the difference in direction, or the amount of opening, between two lines which meet, or tend to meet, in a point. According to this definition no angle can be greater than a straight angle, for obviously the difference in the direction between two lines is greatest when they extend in opposite directions. For the purposes of higher mathematics it is convenient to think of an angle as formed by rotating a line in a plane about a fixed point and to measure its magnitude by the amount of rotation which the line has undergone in forming the angle. If the rotation is in the clockwise direction the angle is considered negative, if in the counter-clockwise direction, positive. Since there is no limit to the amount of rotation which a line may undergo, it is...