Question

What is the exact value of cos(5π/3)?

a) -3√2
b) -√3/2
c) -1/2
d) 1/2

Answer 1

The exact value of cos(5π/3) is determined to be 1/2, correlating to the corresponding angle in the fourth quadrant of the unit circle.

Step-by-step explanation:

The exact value of cos(5π/3) can be determined by considering the unit circle and the properties of the cosine function. The angle 5π/3 radians is equivalent to 300°, which is in the fourth quadrant where cosine values are positive. In this quadrant, the cosine of an angle is the same as the cosine of its reference angle, which is π/3 radians or 60° for this case. The cosine of 60° is 1/2, hence cos(5π/3) is 1/2.