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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