Find the Exact Value sin(210)

Problem

sin(210)

Solution

1. Identify the reference angle by determining how far 210 is from the xaxis.

210−180=30

2. Determine the quadrant in which the angle 210 lies.

180<210<270

The angle is in Quadrant III.

3. Determine the sign of the sine function in Quadrant III.
   In Quadrant III, the ycoordinates are negative, so sin(θ)<0

4. Apply the reference angle and the sign to find the value.

sin(210)=−sin(30)

5. Substitute the known value for sin(30)

sin(30)=1/2

Final Answer

sin(210)=−1/2

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