This is an old revision of the document!

### 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 (° = degrees1), r = radians, g = grads, or d = DMS [DDD.MMSS, where DDD=degrees, MM=minutes, SS=seconds])2). To enter an angle in the 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

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 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 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

1)
The shortcut for the degree symbol is AL-LShold-6
2)
r, g, and d are case insensitive
• manual/chapter3/angles.1564095093.txt.gz