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March 28, 2017

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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)

  • trig - ,

    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.

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