We recall that the polar coordinates are given by the angle and the radius which have the following relationship:
x = r cos (angle)
y = r sin (angle)
so for the case of the point (-8, 6) r is (via Phytagoras theorem) = square root of (64+36) = square root of (100) which is 10.
Then r = 10
now, the angle in our case must be an angle in the SECOND quadrant (notice that x is negative (-8), and y is positive (6)).
then our angle is in between pi/2 and pi
We can use the arc cosine, or arc sine or arc tangent to find the angle:
arc cos(-8/10) = 143.13 degrees
which we can convert to radians by :
143.13 * pi/180 = approx 2.5 radians.
This is indeed an angle in the second quadrant.
Answer: r = 10 and angle = 2.5 radians