Evaluate sin((7pi)/6)

Problem

sin((7*π)/6)

Solution

1. Identify the quadrant of the angle (7*π)/6 Since π<(7*π)/6<(3*π)/2 the angle lies in the third quadrant.

2. Determine the reference angle. The reference angle is calculated as (7*π)/6−π=π/6

3. Apply the sine value for the reference angle. We know that sin(π/6)=1/2

4. Determine the sign of the sine function in the third quadrant. In the third quadrant, the sine function is negative.

5. Combine the sign and the reference value to find the final result.

Final Answer

sin((7*π)/6)=−1/2

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