# TI-BASIC:P Ry

**Command Summary**

P►Ry( calculates the y-value (in Cartesian coordinates) given Polar coordinates.

**Command Syntax**

P►Ry(r,θ)

**Menu Location**

Press:

- 2nd ANGLE to access the angle menu.
- 8 to select P►Ry(, or use arrows and ENTER.

TI-83/84/+/SE

1 byte

P►Ry( (polar to rectangular y-coordinate) calculates the y-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity y=r*sin(θ) is used to calculate P►Ry(.

The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle*180/π and from degrees to radians is angle*π/180. The P►Ry( command also accepts a list of points.

P►Ry(5,π/4) 3.535533906 5*sin(π/4) 3.535533906 P►Ry({1,2},{π/4,π/3}) {.7071067812 1.732050808}

# Advanced Uses

You can bypass the mode setting by using the ° (degree) and ^{r} (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

P►Ry(1,{π/4^^r,60°}) {.7071067812 .8660254038}

# Optimization

In most cases P►Ry(r,θ) can be replaced by r*sin(θ) to save a byte:

:P►Ry(5,π/12) can be :5sin(π/12)

Conversely, complicated expressions multiplied by a sine factor can be simplified by using P►Ry(r,θ) instead.

:(A+BX)sin(π/5) can be :P►Ry(A+BX,π/5)

# Error Conditions

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