Question

Given the polar coordinates of a point, how do I find the rectangular coordinates?

(2, 3pi/4)

(-4, 7pi/6)

(2/3, -2pi/3)

Given the rectangular coordinates of a point, how do I find the polar coordinates?

(4, 0)

(3, 4)

(2, -2)

Answer 1

In (2,3pi/4) r = 2 and the rotation angle is 3pi/4 radians or 135º

make a sketch, draw you angle first, then go out 2 units on that ray.
drop a line to the x-axis, you now have a right-angled triangle in the II quadrant with an outside angle of 135º, and a hypotenuse of 2.
the inside angle is 45º, so it is isosceles.
Use Pythagoras to find each of the sides to be 1
But you are in quadrant II, so the point is (-1,1)
Do the others the same way

For the second type,
plot the point, then make a diagram showing the right-angled triangle.
You will have the x and the y.
Use Pythagoras to find r,
then tan ß = y/x will let you find the angle.