Find the Exact Value sin(-120 degrees )

Problem

sin(−120^∘)

Solution

1. Use the odd function identity for sine, which states that sin(−θ)=−sin(θ)

sin(−120^∘)=−sin(120^∘)

2. Find the reference angle for 120^∘ Since 120^∘ is in the second quadrant, the reference angle is 180^∘−120^∘=60^∘

Reference Angle=60^∘

3. Determine the sign of the sine function in the second quadrant. Since sine is positive in the second quadrant, sin(120^∘)=sin(60^∘)

sin(120^∘)=sin(60^∘)

4. Substitute the known value for sin(60^∘) which is √(,3)/2

sin(60^∘)=√(,3)/2

5. Combine the results to find the final value.

−sin(120^∘)=−√(,3)/2

Final Answer

sin(−120^∘)=−√(,3)/2

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