Find the Exact Value cos((29pi)/6)

Problem

cos((29*π)/6)

Solution

1. Identify the reference angle by finding a coterminal angle within the interval [0,2*π]

2. Divide the numerator by the denominator to determine how many full rotations (2*π or (12*π)/6 are in the angle.

29÷12=2* remainder *5

3. Subtract the full rotations from the original angle.

(29*π)/6−2*(2*π)=(29*π)/6−(24*π)/6

(29*π)/6−(24*π)/6=(5*π)/6

4. Determine the quadrant for the angle (5*π)/6 Since π/2<(5*π)/6<π the angle is in Quadrant II.

5. Apply the cosine sign for Quadrant II. In Quadrant II, cosine values are negative.

6. Find the reference angle for (5*π)/6

π−(5*π)/6=π/6

7. Evaluate the cosine of the reference angle.

cos(π/6)=√(,3)/2

8. Combine the value with the correct sign.

cos((5*π)/6)=−√(,3)/2

Final Answer

cos((29*π)/6)=−√(,3)/2

Want more problems? Check here!