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The unit circle and radians

The unit circle defines sine and cosine for all angles, not just acute ones: the point at angle $v$ from the positive x-axis has coordinates $(\cos v,\sin v)$ . Radians are an alternative way to measure angles, where a full turn is $2\pi$ .

\text{rad} = \text{degrees}\cdot\frac{\pi}{180}

converting between degrees and radians

\sin^2 v + \cos^2 v = 1

the unit circle identity

Symbols

$v$	angle	rad or °
$P$	the point $(\cos v,\sin v)$ on the circle

Example

$210^\circ = 210\cdot\frac{\pi}{180} = \frac{7\pi}{6}\approx 3.67$ rad, and $\sin 210^\circ=-0.5$ .

The sign of

\sin

and

\cos

depends on which quadrant the point

P

is in.

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Part of Foundations of Mathematics: Trigonometry and geometry.