# TI-BASIC:R Pr

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**Command Summary**

R►Pr( calculates the radius component (in polar coordinates) given the Cartesian coordinates.

**Command Syntax**

R►Pr(*x*,*y*)

**Menu Location**

Press:

- 2nd ANGLE to access the angle menu.
- 5 to select R►Pr(, or use arrows and ENTER.

TI-83/84/+/SE

1 byte

R►Pr( (Rectangular to polar radius) takes the (*x*,*y*) (Cartesian) coordinates, and gives the radius coordinate *r* of the same point in (*r*,*θ*) (polar) mode. The identity used for this conversion is *r*² = *x*²+*y*²

R►Pr(3,4) 5 √(3²+4²) 5 R►Pr({6,5},{8,12}) {10 13}

The function works even when the equivalent √(*x*²+*y*²) fails due to overflow:

R►Pr(3e99,4e99) 5e99

# Optimization

R►Pr( is the smallest way to implement the distance formula <math>d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}</math>. Just pass it the values x,,1,,-x,,2,, and y,,1,, - y,,2,, as arguments:

:√((5-2)²+(4-0)²) can be :R►Pr(5-2,4-0)

# Error Conditions

**ERR:DATA TYPE**is thrown if you input a complex argument.**ERR:DIM MISMATCH**is thrown if two list arguments have different dimensions.