It is required to find the exact value of 17π/6 using the unit circle.
To do this, locate the angle on the unit circle to determine the point (x,y) it represents.
Recall that on the unit circle, the cosine is:
[tex]\cos\theta=x[/tex]
Since 17π/6 is greater than 2π, find its equivalent angle that is less than 2π by subtracting multiples of 2π until it is less than 2π:
[tex]\frac{17\pi}{6}-2\pi=\frac{5\pi}{6}[/tex]
Locate this point on the unit circle:
From the unit circle, it can be seen that:
[tex]x=-\frac{\sqrt{3}}{2}\text{ and }y=\frac{1}{2}[/tex]
Hence, the required value is:
[tex]\cos\frac{17\pi}{6}=-\frac{\sqrt{3}}{2}[/tex]
The answer is the first option.
