manual:chapter3:angles [newRPL User Manual]

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===== Angles =====

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==== Entering Angles ====

Angles are their own object type.  An angle is entered by prefixing a number with the angle symbol (∡, shortcut **AL-RS-6**), followed by a number, then finally a suffix that indicates the system (° = degrees((The shortcut for the degree symbol is **AL-LS<sup>hold</sup>-6**)), r = radians, g = grads, or d = DMS [DDD.MMSS, where DDD=degrees, MM=minutes, SS=seconds])((r, g, and d are case insensitive)).  To enter an angle in the [[manual:chapter2:interface|current angle mode of the calculator]], the suffix can be left off.  For example, the following all indicate an angle of 90.5 degrees:

''∡90.5°''

''∡1.5795.r''

''∡100.5556g''

''∡90.3000d''

and

''∡90.5'' with the angle mode set to degrees.


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==== Working with Angles ====

Trigonometric functions operate on angle objects as expected:

''∡45° SIN'' yields the real number result ''0.7071.''

Basic arithmetic operations can also be applied to angle objects:

''∡90° ∡45° +'' yields ''∡135°''

''∡1.57r ∡50° -'' yields ''∡0.6973r''

''∡90° ∡45° *'' yields ''1.2337'' (see below why)

''∡90° ∡45° /'' yields ''2''

The result of an operation on angle objects has the following conventions:

  * Addition and subtraction between angles returns an angle expressed in the system of the first argument. For example ''∡1.57r ∡50° -'' yields ''∡0.6973r''

  * Addition and subtraction between an angle and a real number will interpret the real number as an angle given in the [[manual:chapter2:interface|current angle mode]]. The result will be an angle expressed in the system of the first argument (current mode if the first argument is the real number). For example ''∡90° 45 +'' yields ''∡135°''.

  * Multiplication of an angle by a real number will result in an angle in the given format. For example ''∡90° 2 *''  yields ''∡180°''.

  * Division of an angle by a number results in an angle in the given format. For example ''∡90° 2 /''  yields ''∡45°''.

  * Commands and functions that accept angles as arguments will consider that a real number is an angle expressed in the [[manual:chapter2:interface|current angle mode]]. For example ''90 SIN'' yields ''1'' while the system is in ''DEG'' mode.

  * For all other operations and commands, including those that don't accept angles as arguments, angles will be converted to radians and become normal real numbers. Notice that radians will be used, regardless of the current angle mode. For example ''90 ∡45° /'' yields ''114.591559'', because the angle is converted to radians (notice that while an angle divided by a number is still an angle, the inverse is not true).

  * The system is capable of tracking the behavior mentioned above, therefore if an operation results in an angle being forced into radians, commands that accept angles as arguments (like SIN, COS and TAN) will interpret a number as radians, rather than the current angle mode. For example ''90 ∡45° / SIN'' yields ''0.997'' even when the current angle mode is not radians. When operated in the stack: ''90'' then ''∡45°'', then ''/'' will result in ''114.591559'' and now pressing ''SIN'' will yield ''0.9093'' in ''DEG'' mode, because the number will be considered in the current angle mode.


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==== Commands for Angle Objects ====
| Command | Purpose | Example |
| ''→∡°'' | Convert real number to angle object in degrees. | ''56.2 →∡°'' yields ''∡56.2°'' |
| ''→∡r'' | Convert real number to angle object in radians. | ''56.2 →∡r'' yields ''∡56.2r'' |
| ''→∡g'' | Convert real number to angle object in grads. | ''56.2 →∡g'' yields ''∡56.2g'' |
| ''→∡d'' | Convert real number to angle object in DMS. | ''56.2 →∡d'' yields ''∡56.2d'' |
| ''A→∡°'' | Convert angle to degrees. | ''∡0.7854r. A→∡°'' yields ''∡45.0001.°'' |
| ''A→∡r'' | Convert angle to radians. | ''∡45° A→∡r'' yields ''∡0.7854.r'' |
| ''A→∡g'' | Convert angle to grads. | ''∡45° A→∡g'' yields ''∡50g'' |
| ''A→∡d'' | Convert angle to DMS. | ''∡45.5° A→∡d'' yields ''∡45.3d'' |

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