Question

exact value of sin 210° using the unit circle

Answer 1

so:
sin(120) = sin(30) = -1/2

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OR
180-the angle° = the reference angle.
so:
180 - 210 = -30
so:
sin(-30) = -sin(30) = -(1/2) = -1/2

Answer 2

Use the following guide
1. If the given angle is between 0 and 90 the the given angle is equal to the reference angle
2. If the given angle is between 90 and 180 the reference angle is equal to 180 - given angle
3. If the given angle is between 180 and 270 the reference angle is equal to the given angle - 180
4. If the given angle is between 270 and 360 the reference angle is equal to 360 - given angle
Because the given angle is 210
the reference angle in this case is 210 - 180 = 30
The sign in this case is negative because is in the third quadrant
Sin 210 = - sin (30) = -.5