Find the Exact Value sin(210 degrees )

Problem

sin(210^∘)

Solution

1. Identify the quadrant of the angle. Since 180^∘<210^∘<270^∘ the angle 210^∘ lies in Quadrant III.

2. Determine the sign of the sine function. In Quadrant III, the sine of an angle is negative.

3. Calculate the reference angle. The reference angle θ^′ for an angle in Quadrant III is found using θ^′=θ−180^∘

θ^′=210^∘−180^∘=30^∘

4. Evaluate the sine of the reference angle. The exact value of sin(30^∘) is 1/2

5. Apply the sign from step 2 to the value from step 4.

sin(210^∘)=−sin(30^∘)=−1/2

Final Answer

sin(210^∘)=−1/2

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