give and exact value for cos(2pi/3)
2 pi/3 radians = 360/3 = 120 degrees
180 -120 = 60
so
60 degrees above -y axis in quadrant 2
so
-1/2
To find the exact value of cos(2π/3), we can use the unit circle and the properties of the cosine function.
1. Start by drawing a unit circle, which is a circle centered at the origin with a radius of 1 unit.
2. Divide the unit circle into six equal sections, since there are six trigonometric functions and each section represents a specific angle.
3. The angle 2π/3 is located in the second section counterclockwise from the positive x-axis.
4. In this section, the cosine function is negative. Therefore, we need to find the x-coordinate of the point where the terminal side of the angle intersects the unit circle.
5. By memorizing the important angles of the unit circle, we know that 2π/3 corresponds to the point (-1/2, -√3/2), where the x-coordinate is -1/2.
Thus, the exact value of cos(2π/3) is -1/2.