Find the Exact Value cos(-(4pi)/3)

Problem

cos(−(4*π)/3)

Solution

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

cos(−(4*π)/3)=cos((4*π)/3)

2. Find the reference angle for (4*π)/3 Since the angle is in the third quadrant, subtract π from the angle.

Reference Angle=(4*π)/3−π

Reference Angle=π/3

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

cos((4*π)/3)=−cos(π/3)

4. Evaluate the cosine of the reference angle using known values from the unit circle.

cos(π/3)=1/2

5. Combine the results to find the final exact value.

cos(−(4*π)/3)=−1/2

Final Answer

cos(−(4*π)/3)=−1/2

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