Find the Exact Value sin(-150 degrees )

Problem

sin(−150^∘)

Solution

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

sin(−150^∘)=−sin(150^∘)

2. Find the reference angle for 150^∘ Since 150^∘ is in the second quadrant, the reference angle is 180^∘−150^∘=30^∘

Reference Angle=30^∘

3. Determine the sign of the sine function in the second quadrant. Since sine is positive in the second quadrant, sin(150^∘)=sin(30^∘)

sin(150^∘)=sin(30^∘)

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

sin(30^∘)=1/2

5. Combine the results to find the final value.

−sin(150^∘)=−1/2

Final Answer

sin(−150^∘)=−1/2

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