Answer:
1/2
Step-by-step explanation:
The angle 5pi/3 shows up in the 3rd quadrant and is equivalent to the angle 300 degrees. The "reference angle" of 300 degrees is 60 degrees; the reference angle in this case has the same trig function values as does 300 degrees. Thus, the cosine of 5pi/3 is the same as the cosine of 60 degrees, which is 1/2.
Using equivalent angles, it is found that:
[tex]\cos{\left(\frac{5\pi}{3}\right)} = \frac{1}{2}[/tex]
[tex]\frac{5\pi}{3}[/tex] is an angle in the fourth quadrant, as [tex]\frac{2\pi}{3} \leq \frac{5\pi}{3} \leq 2\pi[/tex].
To find the equivalent in the first quadrant to an angle in the fourth quadrant, we subtract [tex]2\pi[/tex] from the angle, then:
[tex]2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3}[/tex]
Just as in the first quadrant, the cosine is positive in the fourth quadrant, thus, applying the equivalent angle:
[tex]\cos{\left(\frac{5\pi}{3}\right)} = \cos{\left(\frac{\pi}{3}\right)} = \frac{1}{2}[/tex]
A similar problem is given at https://brainly.com/question/23843479
