Find the Exact Value sin(-210 degrees )

Problem

sin(−210^∘)

Solution

1. Use 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, subtract 180^∘ from the angle.

Reference Angle=210^∘−180^∘=30^∘

3. Determine the sign of the sine function in the third quadrant. In the third quadrant, sine is negative.

sin(210^∘)=−sin(30^∘)

4. Substitute the known value for sin(30^∘) which is 1/2

sin(210^∘)=−1/2

5. Apply the negative sign from the first step to find the final value.

−sin(210^∘)=−(−1/2)=1/2

Final Answer

sin(−210^∘)=1/2

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