Find the Exact Value cos(-(11pi)/4)

Problem

cos(−(11*π)/4)

Solution

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

cos(−(11*π)/4)=cos((11*π)/4)

2. Find the coterminal angle within the interval [0,2*π) by subtracting 2*π (which is (8*π)/4 from the argument.

(11*π)/4−(8*π)/4=(3*π)/4

3. Identify the reference angle for (3*π)/4 Since this angle is in the second quadrant, the reference angle is π−(3*π)/4

π−(3*π)/4=π/4

4. Determine the sign of the cosine function in the second quadrant. Cosine is negative in the second quadrant.

cos((3*π)/4)=−cos(π/4)

5. Substitute the known value for cos(π/4) which is √(,2)/2

−cos(π/4)=−√(,2)/2

Final Answer

cos(−(11*π)/4)=−√(,2)/2

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