Find the Exact Value sin(-(5pi)/6)

Problem

sin(−(5*π)/6)

Solution

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

sin(−(5*π)/6)=−sin((5*π)/6)

2. Determine the reference angle for (5*π)/6 Since the angle is in the second quadrant, the reference angle is π−(5*π)/6=π/6

Reference Angle=π/6

3. Identify the sign of the sine function in the second quadrant. Since sine is positive in the second quadrant, sin((5*π)/6)=sin(π/6)

sin((5*π)/6)=1/2

4. Substitute the value back into the expression from step 1.

−sin((5*π)/6)=−1/2

Final Answer

sin(−(5*π)/6)=−1/2

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