find the equation of the line which passes through origin and makes an angle 'a" with line Y=mx+c?

Answer 1

The angle of the line Y = mx + c is arctan(m). Therefore the angle (slope) of the new line is a ± arctan(m); The tangent of this is the slope of the new line, r. Since the line passes through the origin, its equation is

z = r*x

z = tan[a ± arctan(m)]*x

Using the trig formula for tan(A+B), the result is

z = [tan(a) + m]/[1 - m*tan(a)] * x or

z = [tan(a) - m]/[1 + m*tan(a)] * x