Find the Exact Value cos(-(17pi)/3)

Problem

cos(−(17*π)/3)

Solution

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

cos(−(17*π)/3)=cos((17*π)/3)

2. Find the coterminal angle within the interval [0,2*π) by subtracting multiples of 2*π (which is (6*π)/3.

(17*π)/3−2*π=(11*π)/3

(11*π)/3−2*π=(5*π)/3

3. Identify the reference angle for (5*π)/3 in the fourth quadrant.

(θ_ref)=2*π−(5*π)/3

(θ_ref)=π/3

4. Determine the sign of the cosine function in the fourth quadrant. Since cosine is positive in Quadrant IV, the value is the same as cos(π/3)

cos((5*π)/3)=cos(π/3)

5. Evaluate using the unit circle or special right triangles.

cos(π/3)=1/2

Final Answer

cos(−(17*π)/3)=1/2

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