Find the Exact Value cos((-2pi)/3)

Problem

cos(−(2*π)/3)

Solution

1. Apply the even-odd identity for cosine, which states that cos(−θ)=cos(θ)

cos(−(2*π)/3)=cos((2*π)/3)

2. Identify the reference angle for (2*π)/3 by subtracting it from π

π−(2*π)/3=π/3

3. Determine the quadrant of the angle (2*π)/3 which is in Quadrant II.

4. Determine the sign of the cosine function in Quadrant II, which is negative.

cos((2*π)/3)=−cos(π/3)

5. Evaluate the cosine of the reference angle π/3 using the unit circle or special triangles.

cos(π/3)=1/2

6. Combine the sign and value to find the final result.

−1/2

Final Answer

cos(−(2*π)/3)=−1/2

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