[justify]Most readers will be familiar with angles expressed in degrees.  As there are [math]2 \pi [/math] radians in a circle, there are 360 degrees. We denote 360 degrees with the shorthand [math]360^\circ[/math]. If an angle is expressed without the degree symbol ([math]^\circ[/math]), then the angle is in radians. For example, [math]\angle \theta = 20^{\circ}[/math] means angle theta is equal to 20 degrees, but [math]\angle \alpha = 20[/math] means angle alpha is equal to 20 radians.[br] [br]Note that the angle for half of the unit circle is [math]180^{\circ} [/math] and also [math]\pi [/math] rad, so we use the fractions [math]\frac{180^{\circ}} {\pi \text{ rad}} = \frac{\pi \text{ rad}}{180^{\circ}} = 1[/math] to convert between the different units of angle measure.  The technique is known as unit analysis and is useful in all sciences. [br][br]EX:     Convert [math]60^\circ[/math] to radians.[br] [/justify][center][math]60^\circ \cdot \frac{\pi \text{ rad}}{180^{\circ}} = \frac{\pi}{3} [/math] rad.[br] [/center][br]EX:     Convert [math]\frac{3 \pi }{4} [/math] rad to degrees.[br][center][math]\frac{3 \pi }{4} \text{ rad} \cdot \frac{180^{\circ}} {\pi \text{ rad}} = 135^{\circ}[/math][/center]

Fractions of a degree are usually expressed as minutes and seconds.  Just as with time units, there are 60 seconds in a minute and 60 minutes in a degree.   You should be able to convert sub units to degrees with decimals and vice versa using similar unit analysis techniques as above. [br][br]EX:  Convert [math]34.3673^{\circ}[/math] to degrees, minutes, and seconds.[br][br][center][math]\begin{align}34.3673^{\circ} =& 34^{\circ}+0.3673^{\circ} \cdot \frac{60 '}{1 ^{\circ} }\\ =& 34^{\circ} 22.038 ' \\ =& 34^{\circ} 22' + 0.038 '\cdot \frac{60''}{1'} \\ =& 34^{\circ} 22' 2'' \end{align} [/math][/center]Note that this is rounded to the nearest second.   For more precision, just add decimal places to the seconds unit. [br][br][br]EX:  Convert [math]63^{\circ}34'13''[/math] to degrees with decimals.  [br][br][center][math]\begin{align} 63^{\circ}34'13''=& 63^{\circ} + 34' + 13'' \cdot \frac{1'}{60''} \\ =& 63^{\circ} + 34.2167' \cdot \frac{1^{\circ}}{60'} \\ =& 63.57028^{\circ} \end{align}[/math][/center]