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--- manual:chapter3:angles [2017/08/10 18:44]
smartin created
+++ manual:chapter3:angles [2019/07/25 15:51]
claudio [Working with Angles]
@@ Line 5: / Line 5: @@
 ==== Entering Angles ====
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+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.
-==== Working with Angles ====
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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 ''4050''
+''∡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.
+----
 ==== 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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