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The P►Ry( Command

Command Summary Command Syntax Calculator Compatibility Token Size
P►Ry( calculates the y-value (in Cartesian coordinates) given Polar coordinates. P►Ry(r,θ) TI-83/84/+/SE 1 byte

Press:
1. 2nd ANGLE to access the angle menu.
2. 8 to select P►Ry(, or use arrows and ENTER.

The P►Ry( Command

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

Authors: KG