Simplify cos((5pi)/6)

Problem

cos((5*π)/6)

Solution

1. Identify the quadrant of the angle (5*π)/6 Since π/2<(5*π)/6<π the angle is in the second quadrant.

2. Determine the sign of the cosine function in the second quadrant. In the second quadrant, the cosine of an angle is negative.

3. Find the reference angle. The reference angle (θ_r*e*ƒ) is calculated by subtracting the angle from π

(θ_r*e*ƒ)=π−(5*π)/6

(θ_r*e*ƒ)=π/6

4. Evaluate the cosine of the reference angle. Using the unit circle or special triangles, the value is known.

cos(π/6)=√(,3)/2

5. Apply the sign from step 2 to the value from step 4.

cos((5*π)/6)=−√(,3)/2

Final Answer

cos((5*π)/6)=−√(,3)/2

Want more problems? Check here!