Find the Exact Value sin(-(7pi)/6)

Problem

sin(−(7*π)/6)

Solution

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

sin(−(7*π)/6)=−sin((7*π)/6)

2. Identify the reference angle for (7*π)/6 Since (7*π)/6=π+π/6 the angle is in the third quadrant and the reference angle is π/6

Reference Angle=π/6

3. Determine the sign of the sine function in the third quadrant. Since sine is negative in the third quadrant, sin((7*π)/6)=−sin(π/6)

−sin((7*π)/6)=−(−sin(π/6))

4. Simplify the signs and evaluate the sine of the reference angle using the unit circle or special triangles, where sin(π/6)=1/2

−(−1/2)=1/2

Final Answer

sin(−(7*π)/6)=1/2

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