7
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My counterpart has committed multiple crimes;

Square us and add: the result is not prime.

You use me for a reason;

I'm not liked by Cartesians;

My converse is a measurement of time.

What am I?

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  • 1
    $\begingroup$ Good riddle! Please make more of these :) $\qquad (+1)$ $\endgroup$ – Mr Pie Jul 1 '18 at 0:31
9
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My angle on this is you are:

$\cos$

My counterpart has committed multiple crimes;

Your counterpart is $\sin$ and this commits multiple crimes.

Square us and add: the result is not prime.

Squaring and adding you and your counterpart,
$$\sin^2\theta + \cos^2\theta = 1$$ which is not included as a prime number.

You use me for a reason;

Cos sounds like cause - thanks to Mea Culpa Nay.

I'm not liked by Cartesians;

You are used for angle based coordinates systems such as polar and not Cartesian.

My converse is a measurement of time.

Converse meaning reciprocal gives the $\sec$ function.

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