When trying to identify angles on the unit circle with their corresponding sine and cosine value, there is an easy way to do this.

Remember that the angles start at 0, then 30, 45, 60, 90 in the first quadrant. So they angle increases by 30, 15, 15 and 30. Likewise they increase by the same amount in the 2nd , 3rd and 4th quadrants.

So the remaining angles on the unit circle are 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, 360.

The sine and cosine values in the first quadrant are 1/2, sqrt(2)/2, sqrt(3), 2 - Sine

sqrt(3)/2, sqrt(2)/2, 1/2 - Cosine

These values remain the same in all quadrants with the exception of + or -.

Just remember the signs are follows

Quadrant, Sine, Cosine

1 + +

II + -

III - -

IV - +

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