Find the Exact Value 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 Quadrant III.

2. Determine the reference angle. The reference angle θ′ for an angle in Quadrant III is calculated as θ−π

θ′=(7*π)/6−π=π/6

3. Apply the sign of the sine function in Quadrant III. In Quadrant III, the sine of an angle is negative.

sin((7*π)/6)=−sin(π/6)

4. Evaluate the sine of the reference angle. Using the unit circle or special triangles, sin(π/6)=1/2

sin((7*π)/6)=−1/2

Final Answer

sin((7*π)/6)=−1/2

Want more problems? Check here!