Quandaries and Queries


Who is asking: Parent
Level: All

I am trying to help my son with his home, but I don't remember these conversions. Please help.

1. Convert the following coordinates
Cartesian x = 7, y = -24

2. Convert the following coordinates
Polar r = 4, theta = pi / 3




I do it with a diagram.

In polar coordinates r is the distance |OP| and theta is the angle that the line OP makes with the positive x-axis, usually measured counterclockwise. When P is (7, -24),

|OP| = sqrt(72 + 242) = 25

To find theta I looked at the diagram below.

The measure of the angle POQ is tan-1(|QP|/|OQ|) = 73.74o. Thus theta, the angle QOP in the first diagram is 360o - 73.740 = 286.26o. (Maybe you want this in radians.)

For the second [art again draw a diagram.

Since |OP| = 4 and angle POQ is pi/3, |OQ| = 4 cos(pi/3) = 2 and |QP = 4 sin(pi/3) = 2 sqrt(3).




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