# TI-BASIC:R Ptheta

**Command Summary**

R►Pθ( calculates the angle coordinate (in polar coordinates) given the Cartesian coordinates.

**Command Syntax**

R►Pθ(*x*,*y*)

**Menu Location**

Press:

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

TI-83/84/+/SE

1 byte

R►Pθ( (Rectangular to polar θ) takes the (*x*,*y*) (Cartesian) coordinate, and returns the angle that the ray from (0,0) to (*x*,*y*) makes with the positive x-axis. This is the θ-coordinate of the same point in (*r*,*θ*) (polar) mode. The identity used for this conversion is tan(*θ*)=*y*/*x*, with the correct inverse being chosen depending on the quadrant that the point is in. The range of the angle returned is -π<*θ*≤π. R►Pθ( can also be used on lists.

R►Pθ( is equivalent to the atan2() instruction seen in C/++ and FORTRAN.

R►Pθ(3,4) .927295218 tanֿ¹(4/3) .927295218 R►Pθ(0,{1,-1}) {1.570796327, -1.57096327}

R►Pθ( is affected by Degree and Radian mode in its output, which is an angle measured in degrees or radians respectively.

# Advanced Uses

If you want the result to always be a radian angle, regardless of mode settings, you can divide the result by 1^{r}:

R►Pθ(x,y)/1^^r

If you want the result to always be a degree angle, regardless of mode settings, you can divide the result by 1°:

R►Pθ(x,y)/1°

# 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.