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

Problem

cos(−(2*π)/3)

Solution

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

cos(−(2*π)/3)=cos((2*π)/3)

2. Identify the reference angle for (2*π)/3 Since the angle is in the second quadrant, the reference angle is π−(2*π)/3=π/3

(θ_ref)=π/3

3. Determine the sign of the cosine function in the second quadrant. In the second quadrant, cosine values are negative.

cos((2*π)/3)=−cos(π/3)

4. Substitute the known value for cos(π/3) which is 1/2

−cos(π/3)=−1/2

Final Answer

cos(−(2*π)/3)=−1/2

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