Final answer:
The value of the given trigonometric functions os 7π/6 is -√3/2.
Step-by-step explanation:
To find the value of cos(7π/6), we can use the unit circle.
The angle 7π/6 is in the third quadrant, so the cosine function will be negative.
The reference angle is π/6, which corresponds to a 30-degree angle in the first quadrant.
Since the cosine function is negative in the third quadrant, we know that cos(7π/6) = -cos(π/6).
The value of cos(π/6) is √3/2, so cos(7π/6) = -√3/2.
So therefore the value of cos(7π/6) is -√3/2.