Find the Exact Value cos((17pi)/6)

Problem

cos((17*π)/6)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

(17*π)/6−2*π=(17*π)/6−(12*π)/6

(17*π)/6−(12*π)/6=(5*π)/6

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

3. Determine the sign of the cosine function in Quadrant II. In this quadrant, cosine values are negative.

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

π−(5*π)/6=π/6

5. Evaluate the cosine of the reference angle using known trigonometric values.

cos(π/6)=√(,3)/2

6. Apply the sign from step 3 to the value found in step 5.

cos((5*π)/6)=−√(,3)/2

Final Answer

cos((17*π)/6)=−√(,3)/2

Want more problems? Check here!