Property	Value
Hex Value	`$1E`
Categories	Angle Catalog > P
Localizations	FR: `P►Ry(`

`P►Ry(`

Overview

Returns Y, given polar coordinates r and θ or a list of polar coordinates.

Availability: Token available everywhere.

Syntax

P►Ry(r,θ)

Arguments

Name	Type	Optional
r
θ

Location

2nd, angle, ANGLE, 8:P, Ry(

Description

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 angle180/π and from degrees to radians is angleπ/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.

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, thornahawk.

History

Calculator	OS Version	Description
TI-82	1.0	Added

Authors: Adrien Bertrand

P►Ry(