Find the Exact Value cos(-(17pi)/6)

Problem

cos(−(17*π)/6)

Solution

1. Use the even-odd property of the cosine function, which states that cos(−θ)=cos(θ)

cos(−(17*π)/6)=cos((17*π)/6)

2. Find a coterminal angle by subtracting multiples of 2*π (which is (12*π)/6 until the angle is within the interval [0,2*π)

(17*π)/6−(12*π)/6=(5*π)/6

3. Determine the reference angle for (5*π)/6 which is located in the second quadrant.

π−(5*π)/6=π/6

4. Apply the cosine value for the reference angle π/6 and determine the sign based on the quadrant. Since the angle is in Quadrant II, the cosine value is negative.

cos((5*π)/6)=−cos(π/6)

5. Substitute the known value for cos(π/6)=√(,3)/2

−√(,3)/2

Final Answer

cos(−(17*π)/6)=−√(,3)/2

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