Find the Value Using the Unit Circle sin((11pi)/6)

Problem

sin((11*π)/6)

Solution

1. Identify the position of the angle (11*π)/6 on the unit circle.

2. Determine the quadrant by comparing the angle to 2*π Since (11*π)/6 is slightly less than (12*π)/6=2*π the angle is in Quadrant IV.

3. Find the reference angle by subtracting the angle from 2*π

Reference Angle=2*π−(11*π)/6

Reference Angle=π/6

4. Recall the sine value for the reference angle π/6

sin(π/6)=1/2

5. Apply the sign for Quadrant IV. In Quadrant IV, the ycoordinate (sine) is negative.

sin((11*π)/6)=−1/2

Final Answer

sin((11*π)/6)=−1/2

Want more problems? Check here!