How to Find Exact Values on the Unit Circle

On the unit circle, a point is $(cos θ, sin θ)$ . Most values come from $\frac{π}{6}$ , $\frac{π}{4}$ and $\frac{π}{3}$ .

Worked examples

Reference angle: $\frac{π}{3}$

Sine is positive in Quadrant II.

$sin \frac{2 π}{3} = \frac{3}{2}$

Reference angle: $\frac{π}{6}$

Cosine is negative in Quadrant II.

$cos \frac{5 π}{6} = - \frac{3}{2}$

Treating every value in Quadrant II as negative.

Cosine is negative there, but sine is positive. Remember that $x$ is cosine and $y$ is sine.

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