Defining Degree & Radians

L2MAEL

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We use ‘degrees’, when measuring angles, or when we’re doing trigonometry to find the unknown angle ${(}^o)$.

However, there is another way to measure angles, which is called the radians; the setting which gives you the negative angles when you’re doing trigonometry.

1 radian can be found when the arc of a circle has equal length to the radius of the same circle:

Source: https://darkpgmr.tistory.com/26

1 radian is approximately $57.3^o$, and we can see from here 1 radian is significantly greater than 1 degrees.

So, what is the relationship between degrees and radians? $1\text{ radian}=\frac{180}{\pi \text{ degrees}}$, and when rearranged, you can find the radian for 1 degrees:

$1\text{ degrees}=\frac{\pi }{180\text{ radian}}$

Using this, we can find that $360^o=2\pi \text{ radian}$, and thus meaning that $180^o=\pi \text{ radian}$.

Here are some formulas that may be helpful:

$180^o=\pi \text{ radian}$

$1^o=\frac{\pi }{180}\text{ radian}$

$x^o=\frac{x\pi }{180}\text{ radian}$

$\pi \text{ radian}=180^o$

$1\text{ radian}={\frac{180}{\pi }}^o$

$x\text{ radian}={\frac{180x}{\pi }}^o$