Help converting coordinates to polar coordinate form?

well you would want to find the angles in radians of each point from 0 in the unit circle  you can find the angles by drawing triangles and solving for the angles with your calculator if needed (adding 90 or 180 if needed to find the angle in degrees)  you know the length r simply by using pythagorean theorm. (a^2 + b^2 = c^2)

for instance for the first one.  
the point 1,1 is in the 1st quandrant.  if you were to draw that point and make a right triangle from it. you would find that it's length is 1, it's height is 1, and it's hypotenuese (r) is the square root of 2.  it is a 45 degree angle from the positive x axis (where zero on the unit circle is)  45 degrees is also pi/4 radians.  since polar form is in the form (r, theta [angle]) the answer to the first one is (root 2 , pi/4)

The other ones may require the use of a calculator to find the angle.  But you can find r by use of the pythagorean theorm.

It's not too hard, i'm sorry to say i may not be able to explain this too well, but i hope this helps.

Polar coordinates are in the form (r, theta)

In order to find r, its how long (1,1), (3,6), and (-5,1) is from the origin so

r = square root of ((1-0)^2 + (1-0)^2) which is square root of 2
etc.

To find theta, you want to find the angle so you can just draw a triangle and use

arc tan-1(y/x) where y/x is 1/1, 3/6, and -5,1