Find the exact value of the trigonometric function at the given real number, if it exists:tan 17pi/6
First, we need to find the reference angle for 17π/6. To find the reference angle, we subtract multiples of 2π until we get a positive angle less than 2π:
17π/6 - 2π = 17π/6 - 12π/6 = 5π/6
Now, we need to determine in which quadrant the angle 17π/6 lies in. Since 5π/6 is in the second quadrant (between π/2 and π), the tangent function is negative in this quadrant.
Now, we can find the exact value of the tangent of 17π/6 by finding the tangent of the reference angle (5π/6) in the second quadrant:
tan(5π/6) = -√3
Therefore, the exact value of tan(17π/6) is -√3.