Find the Value Using the Unit Circle sin((7pi)/6)

Problem

sin((7*π)/6)

Solution

1. Identify the location of the angle (7*π)/6 on the unit circle. Since π<(7*π)/6<(3*π)/2 the angle is located in Quadrant III.

2. Calculate the reference angle θ^′ by subtracting π from the given angle.

θ^′=(7*π)/6−π

θ^′=π/6

3. Determine the sine value of the reference angle.

sin(π/6)=1/2

4. Apply the sign for Quadrant III. In the third quadrant, the ycoordinate (sine) is negative.

sin((7*π)/6)=−1/2

Final Answer

sin((7*π)/6)=−1/2

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