Radian

Table of Contents

Another unit of measurement alternate to the Degrees method.

Radian

Arc Length

The arc length is the length of the curved part. Example: Red one is the arc length

Arc Length Subtended By angle

The arc length, opposite to the angle Where is your angle? trace it and find the opposite length dumbass

Measurement origins

The official definition is: The angle subtended from the centre of the circle which intercepts an arc in equal length to the radius How it was originated results in trying to measure an angle, through counting the number of radius-arc-pairs a circle can have. a radius-arc-pair ← my pseudoterm is when an angle’s arc length subtending it is the same length as the radius. Example: r = r What they found out was that this was actually a constant. For every circle, no matter the radius, there are exactly $2\pi$ radians

Dont overcomplicate it, its just a unit of measurement.

Formula

a = r * $\theta$ a : arc length r : radius $\theta$ : angle in radians

Does this make sense? A radian is when arc length = radius So radian = arc length / radius = a/r

Radians to Angle

Degree → Radian

degree angle * $\frac{\pi }{180}$

Radian → Degree

radian angle * $\frac{180}{\pi }$

Angular Velocity

Angular velocity of an object is given as the amount of rotation around a central point per unit of time. The amount of ration may be a expression of degrees or radians

Revolution In degrees / radians

To degrees: revolutions * 360 To radians: revolutions * 2pi Does this make sense?

Radian Memorization

${\theta }^o$	${\theta }_{rad}$	sin$\theta$	cos$\theta$	tan$\theta$
$30^o$	$\frac{\pi }{6}$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{3}}$
$60^o$	$\frac{\pi }{3}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$
$90^o$	$\frac{\pi }{2}$	$1$	$0$	$undefined$