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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