Find the Value Using the Unit Circle cos((2pi)/3)

Problem

cos((2*π)/3)

Solution

1. Identify the angle (2*π)/3 on the unit circle. This angle is located in the second quadrant because π/2<(2*π)/3<π

2. Determine the reference angle by subtracting the angle from π

Reference Angle=π−(2*π)/3

Reference Angle=π/3

3. Recall the cosine value for the reference angle π/3 from the unit circle.

cos(π/3)=1/2

4. Apply the sign based on the quadrant. In the second quadrant, the xcoordinate (cosine) is negative.

cos((2*π)/3)=−1/2

Final Answer

cos((2*π)/3)=−1/2

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