====== Radians and Degrees ======
===== Definitions =====
==== Standard Position ====
An angle is in standard position if the initial side of the angle is on the x-axis between the 1st and 4th quarter.
==== Positive Angle ====
An angle that extends counterclockwise((a common misconception is that angles are positive when rotated clockwise, the standard in mathematics is the opposite)).
==== Negative Angle ====
An angle that extends clockwise.
==== Coterminal Angle ====
Equivalent angle that has a different numerical value. Add or subtract $360$ for degrees and $2\pi$ for radians to get a coterminal angle.

===== Degrees =====
Degrees is an angle measurement where one full revolution is 360.

==== Degrees Minutes Seconds ====
Instead of a decimal representation, degrees can also be specified in minutes and seconds, akin to standard time((which supposedly degrees are [[https://en.wikipedia.org/wiki/Degree_(angle)#History|based on]])). The conversion to decimal is $x + \frac{y}{60} + \frac{z}{3600}$ where x is whole unit degrees, y is minutes((denoted by ' mark/foot mark)), and z is seconds((denoted by " mark/inches mark)).

===== Radians =====
A radian is a measurable length where the radius of a circle equals to an arc length section of the circle. $r = s$ where $r$ is the radius and $s$ is the arc length segment.

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===== Converting Rad to Deg and vice versa =====
The conversion is $\pi = 180$ degrees.
Degree to **Radian**: $d * \frac{\pi}{180} = r$
Radian to **Degree**: $r * \frac{180}{\pi} = d$

===== Complementary and Supplementary Angles =====
  * Angles are complementary when they sum up to 90° or $\frac{\pi}{2}$
  * Angles are supplementary when they sum up to 180° or $\pi$