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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