Question

Find the polar coordinates for the point (-8,6). Please help, I think a tutor got the answer wrong and I want to verify with another tutor. thank you

Answer 1

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