Find the Value Using the Unit Circle cos((5pi)/3)

Problem

cos((5*π)/3)

Solution

1. Identify the angle (5*π)/3 on the unit circle.

2. Determine the quadrant by comparing the angle to the axes. Since (3*π)/2<(5*π)/3<2*π the angle is in Quadrant IV.

3. Calculate the reference angle θ′ using the formula for Quadrant IV: θ′=2*π−θ

θ′=2*π−(5*π)/3=π/3

4. Evaluate the cosine of the reference angle.

cos(π/3)=1/2

5. Determine the sign of the cosine function in Quadrant IV. In Quadrant IV, the xcoordinate (cosine) is positive.

cos((5*π)/3)=1/2

Final Answer

cos((5*π)/3)=1/2

Want more problems? Check here!