Simplify cos((7pi)/6)

Problem

cos((7*π)/6)

Solution

1. Identify the quadrant of the angle (7*π)/6 Since π<(7*π)/6<(3*π)/2 the angle lies in Quadrant III.

2. Determine the sign of the cosine function in Quadrant III. In this quadrant, the xcoordinates are negative, so cos((7*π)/6) must be negative.

3. Find the reference angle (θ_R) by subtracting π from the given angle.

(θ_R)=(7*π)/6−π

(θ_R)=π/6

4. Evaluate the cosine of the reference angle using standard trigonometric values.

cos(π/6)=√(,3)/2

5. Apply the sign from Quadrant III to the reference value.

cos((7*π)/6)=−√(,3)/2

Final Answer

cos((7*π)/6)=−√(,3)/2

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