The choices involve either 72° or 108°, neither of which
are special angles, so to get those answers is going to
take some high powered trigonometry. So the easiest way
to get the correct answer it to take an arbitrary
point on the line –2x + 6y = 9, convert it to polar form,
substitute it in the four answers and see which one, if
any, it checks in.
–2x + 6y = 9
If x = -4.5, y=0, that's the x-intercept.
So (-4.5,0) is a rectangular point on the given line.
The rectangular point (-4.5,0)
is the same as the polar point
(r,Ө) = (4.5,180°)
The choices are:
7√(10)/20 = r cos(Ө – 72°)
9√(10)/20 = r cos(Ө – 72°)
9√(10)/20 = r cos(Ө – 108°)
7√(10)/20 = r cos(Ө – 108°)
The left sides of the first and last choices
are the same 7√(10)/20 = 1.106797181
The left sides of the second and third choices
are the same 9√(10)/20 = 1.423024947
If we substitute r=4.5 and Ө=180°, the right
side of the first two choices
gives -1.390576475
If we substitute the same in the right side of the
last two choices we get 1.390576475.
So none of those answers can possibly be correct!!!
Edwin
