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

Problem

cos(2/3*π)

Solution

1. Identify the angle (2*π)/3 in terms of degrees to better visualize its position on the unit circle.

(2*π)/3⋅180^∘/π=120^∘

2. Determine the quadrant where the angle terminates. Since 90^∘<120^∘<180^∘ the angle is in Quadrant II.

3. Find the reference angle θ^′ by subtracting the angle from π

θ^′=π−(2*π)/3=π/3

4. Apply the cosine value for the reference angle π/3 (or 60^∘.

cos(π/3)=1/2

5. Determine the sign of the cosine function in Quadrant II. In Quadrant II, xcoordinates are negative, so cosine is negative.

cos((2*π)/3)=−cos(π/3)

6. Substitute the known value to find the final result.

cos((2*π)/3)=−1/2

Final Answer

cos(2/3*π)=−1/2

Want more problems? Check here!