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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