Simplify sin(-210)

Problem

sin(−210^∘)

Solution

1. Apply the odd function property of the sine function, which states that sin(−θ)=−sin(θ)

sin(−210^∘)=−sin(210^∘)

2. Find the reference angle for 210^∘ Since 210^∘ is in the third quadrant, the reference angle is 210^∘−180^∘=30^∘

Reference Angle=30^∘

3. Determine the sign of the sine function in the third quadrant. Since sine is negative in the third quadrant, sin(210^∘)=−sin(30^∘)

−sin(210^∘)=−(−sin(30^∘))

4. Simplify the expression by applying the double negative and using the known value sin(30^∘)=1/2

−(−sin(30^∘))=sin(30^∘)

5. Evaluate the final result.

sin(30^∘)=1/2

Final Answer

sin(−210^∘)=1/2

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