Find the Exact Value 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 is in the third quadrant.

2. Determine the reference angle. For an angle θ in the third quadrant, the reference angle θ′ is calculated as θ−π

θ′=(7*π)/6−π

θ′=π/6

3. Recall the cosine value for the reference angle. The exact value of cos(π/6) is √(,3)/2

4. Apply the sign for the third quadrant. In the third quadrant, the cosine function is negative.

cos((7*π)/6)=−cos(π/6)

5. Substitute the known value to find the final result.

cos((7*π)/6)=−√(,3)/2

Final Answer

cos((7*π)/6)=−√(,3)/2

Want more problems? Check here!