Name: Trig functions and the unit circle: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 46 s
Description: What is the exact value of cos 210°? Try it, then watch the animated solution.

On the unit circle,

\cos\theta

is the

x

-coordinate of the point reached by turning through

\theta

.

Turn

210^\circ

. That is

30^\circ

past

180^\circ

, so the point is in the third quadrant,

30^\circ

below the

x

-axis.

Drop a line to the

x

-axis. The triangle is 30-60-90 with hypotenuse

1

, so its legs are

\tfrac{1}{2}

and

\tfrac{\sqrt{3}}{2}

.

The point is left of the

y

-axis, so its

x

-coordinate is negative:

\cos 210^\circ = {-\tfrac{\sqrt{3}}{2}}

.

Traps:

{-\tfrac{1}{2}}

is the sine,

\tfrac{\sqrt{3}}{2}

forgets the sign, and

\tfrac{1}{2}

makes both mistakes.

Try it first