Find the Exact Value cos(-(7pi)/6)

Problem

cos(−(7*π)/6)

Solution

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

cos(−(7*π)/6)=cos((7*π)/6)

2. Identify the reference angle by determining the position of (7*π)/6 on the unit circle. Since π<(7*π)/6<(3*π)/2 the angle is in Quadrant III.

Reference Angle=(7*π)/6−π=π/6

3. Determine the sign of the cosine function in Quadrant III. Since the x-coordinates are negative in the third quadrant, the value must be negative.

cos((7*π)/6)=−cos(π/6)

4. Evaluate the cosine of the reference angle π/6 using known trigonometric values.

cos(π/6)=√(,3)/2

5. Combine the results to find the exact value.

cos(−(7*π)/6)=−√(,3)/2

Final Answer

cos(−(7*π)/6)=−√(,3)/2

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