grade 12 · PRE-002

Read a unit-circle coordinate

Use reference angles and quadrant signs to identify exact coordinates.

Learn togetherFresh problem · seed 983656771

Which point on the unit circle corresponds to \(30^\circ\)?

Let's work it out together.

Work through one checkpoint at a time. Your answer area opens after the reasoning.

Checkpoint 1

Find the reference angle.
Checkpoint 2

Use \((x,y)=(\cos\theta,\sin\theta)\).
Checkpoint 3

Apply the coordinate signs for the angle quadrant.

\(\left(\frac{\sqrt2}{2},\frac{\sqrt2}{2}\right)\)\(\left(\frac12,\frac{\sqrt3}{2}\right)\)\(\left(-\frac12,\frac{\sqrt3}{2}\right)\)\(\left(\frac{\sqrt3}{2},\frac12\right)\)