Coordinate Conversions The function names for these conversions are y,x θ,r and θ,r y,x. Polar coordinates (r,θ) and rectangular coordinates (x,y) are measured as shown in the illustration. The angle θ uses units set by the current angular mode. A calculated result for θ will be between –180° and 180°, between –π and π radians, or between –200 and 200 grads.
To convert between rectangular and polar coordinates: 1.
Enter the coordinates (in rectangular or polar form) that you want to convert. In RPN mode, the order is y Ï x or θ Ï r.
2. Execute the conversion you want: press ¹ ° (rectangular–to–polar) or º ± (polar–to–rectangular). The converted coordinates occupy the X– and Y–registers. 3. The resulting display (the X–register) shows either r (polar result) or x (rectangular result). Press w to see θ or y.
y, x
Y X
y
θ
x
r θ, r
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θ, r
y, x
Real–Number Functions
File name 33s-English-Manual-040130-Publication(Edition 2).doc Printed Date : 2004/1/30 Size : 13.7 x 21.2 cm
Page : 388
Example: Polar to Rectangular Conversion.
In the following right triangles, find sides x and y in the triangle on the left, and hypotenuse r and angle θ in the triangle on the right.
10
r
y
4
θ
30 o
x
3
Keys:
Ý { } 30 Ï 10 º ± w 4Ï3¹° w
Display:
Description:
Sets Degrees mode.
Calculates x.
Displays y.
Calculates hypotenuse (r).
Displays θ.
Example: Conversion with Vectors.
Engineer P.C. Bord has determined that in the RC circuit shown, the total impedance is 77.8 ohms and voltage lags current by 36.5º. What are the values of resistance R and capacitive reactance XC in the circuit? Use a vector diagram as shown, with impedance equal to the polar magnitude, r, and voltage lag equal to the angle, θ, in degrees. When the values are converted to rectangular coordinates, the x–value yields R, in ohms; the y–value yields XC , in ohms.
Real–Number Functions File name 33s-English-Manual-040130-Publication(Edition 2).doc Printed Date : 2004/1/30 Size : 13.7 x 21.2 cm
Page : 388
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