...Е. Ex. 3. у — x ='0 ; let« =r О Л у = 0, and the line passes through the origin ; also a or the tangent of the angle which the line makes with the axis o( x =: 1, therefore that angle = 45°; hence the straight line drawn through the origin and bisecting...

...appropriated to the former by substituting, (11,) — -fL for m, and — .£ for h . . , . ob 14. Since, (12,) m is the tangent of the angle which the line makes with the axis of x, by calling this angle u, the equation of the line may be expressed thus : y = x tan u -j- h, 15. When...

...rectangular, but if they be oblique, the coefficient of x, in the equation to a straight line, is not the tangent of the angle which the line makes with the axis of л. Let w = the angle between the axes, в = the angle which the line makes with the axis of x ; y...

...coefficient of either variable be made equal to unity, the coefficient of the other variable will be the tangent of the angle which the line makes with the axis of that variable ; and the absolute term will be the distance cut off from the axis of that variable whose...

...Lacroiafs Trigonometrie, and other similar works. The equation to a straight line is y = ax + b: where a is the tangent of the angle which the line makes with the axis of x, and 6 is the distance from the origin at which it intersects the axis of y. 31 . Let a, a be the abscissas,...

...Lacroix's Trigonometric, and other similar works. The equation to a straight line is y = ax + b : where o is the tangent of the angle which the line makes with the axis of a?, and b is the distance from the origin at which it intersects the axis of y. 31. Let a, a' be the...

...coefficient of either variable be made equal to unity, the coefficient of the other variable will be the tangent of the angle which the line makes with the axis of that variable ; and the absolute term will be the distance cut off from the axis of that variable whose...

...+ c, multiply by cos 0, and put с cos 0 = p, it assumes the form у cos 0 - x sin 0 = p. Here 0 is the angle which the line makes with the axis of x ; and, if we draw OQ perpendicular to AB, p = OQ ; for p = с cos 0 = OB cos BOO. = OQ. * This equation may...

...-- 5- ; m2a2= a*y LI _ .'. A/»w2a2+62= — ; substituting these values, . . . (2) ; where m must be the tangent of the angle which the line makes with the axis ofa;. This form of the equation to the tangent is often convenient in the solution of problems. As...

...represents a straight line passing through the origin, since x = 0, gives y = 0. Now, the coefficient of x is the tangent of the angle which the line makes with the axis of x. Hence, if 9X be the angle which (1) makes with axis, and 62 be the angle which (2) makes with the same,...