Find the equation of the line which passes through the point (-2,3) and makes an angle 60 with the positive direction of x axis .

For solving the problem, we'll use the next working rule:
the equation of the line which passes through a given point and has an inclination "a"
is:

(x-x1) / cos a = (y-y1) / sin a =
r,

 where (x1,y1) are the coordinates of the
given point and r is the distance between (x,y) and
(x1,y1).

In our case, the coordinates of the given
point (-2,3) and the inclination a = 60 degrees.

The
equation is:

[x-(-2)]/cos 60 = (y-3)/ sin 60
= r

cos 60 = 1/2 and sin 60 =
sqrt3/2

(x+2)/(1/2) =
(y-3)/(sqrt3/2)

We'll divide by
2:

x+2 = (y-3)/sqrt 3 =
r/2